Publications
105 results found
Xiao D, Fang F, Heaney CE, et al., 2019, A domain decomposition method for the non-intrusive reduced order modelling of fluid flow, Computer Methods in Applied Mechanics and Engineering, Vol: 354, Pages: 307-330, ISSN: 0045-7825
In this paper we present a new domain decomposition non-intrusive reduced order model (DDNIROM) for the Navier–Stokes equations. The computational domain is partitioned into subdomains and a set of local basis functions is constructed in each subdomain using Proper Orthogonal Decomposition (POD). A radial basis function (RBF) method is then used to generate a set of hypersurfaces for each subdomain. Each local hypersurface represents, not only the fluid dynamics over the subdomain to which it belongs, but also the interactions with the surrounding subdomains. This implicit coupling between the subdomains provides the global coupling necessary to enforce incompressibility and is a means of providing boundary conditions for each subdomain.The performance of this DDNIROM is illustrated numerically by three examples: flow past a cylinder, and air flow over 2D and 3D street canyons. The results show that the DDNIROM exhibits good agreement with the high-fidelity full model while the computational cost is reduced by several orders of magnitude. The domain decomposition (DD) method provides the flexibility to choose different numbers of local basis functions for each subdomain depending on the complexity of the flow therein. The fact that the RBF surface representation takes input only from its current subdomain and the surrounding subdomains, means that, crucially, there is a reduction in the dimensionality of the hypersurface when compared with a more traditional, global NIROM. This comes at the cost of having a larger number of hypersurfaces.
Hu R, Fang F, Pain CC, et al., 2019, Rapid spatio-temporal flood prediction and uncertainty quantification using a deep learning method, Journal of Hydrology, Vol: 575, Pages: 911-920, ISSN: 0022-1694
Recently accrued attention has been given to machine learning approaches for flooding prediction. However, most of these studies focused mainly on time-series flooding prediction at specified sensors, rarely on spatio-temporal prediction of inundations. In this work, an integrated long short-term memory (LSTM) and reduced order model (ROM) framework has been developed. This integrated LSTM-ROM has the capability of representing the spatio-temporal distribution of floods since it takes advantage of both ROM and LSTM. To reduce the dimensional size of large spatial datasets in LSTM, the proper orthogonal decomposition (POD) and singular value decomposition (SVD) approaches are introduced. The LSTM training and prediction processes are carried out over the reduced space. This leads to an improvement of computational efficiency while maintaining the accuracy. The performance of the LSTM-ROM developed here has been evaluated using Okushiri tsunami as test cases. The results obtained from the LSTM-ROM have been compared with those from the full model (Fluidity). In predictive analytics, it is shown that the results from both the full model and LSTM-ROM are in a good agreement whilst the CPU cost using the LSTM-ROM is decreased by three orders of magnitude compared to full model simulations. Additionally, prescriptive analytics has been undertaken to estimate the uncertainty in flood induced conditions. Given the time series of the free surface height at a specified detector, the corresponding induced wave conditions along the coastline have then been provided using the LSTM network. Promising results indicate that the use of LSTM-ROM can provide the flood prediction in seconds, enabling us to provide real-time predictions and inform the public in a timely manner, reducing injuries and fatalities.
Steppeler J, Li J, Fang F, et al., 2019, o3o3: A variant of spectral elements with a regular collocation grid, Monthly Weather Review, Vol: 147, Pages: 2067-2082, ISSN: 0027-0644
In this study, an alternative local Galerkin method (LGM), the o3o3 scheme, is proposed. o3o3 is a variant or generalization of the third-order spectral element method (SEM3). It uses third-order piecewise polynomials for the representation of a field and piecewise third-degree polynomials for fluxes. For the discretization, SEM3 uses the irregular Legendre–Gauss–Lobatto grid while o3o3 uses a regular collocation grid. o3o3 can be regarded as an inhomogeneous finite-difference scheme on a uniform grid, which means that the finite-difference equations are different for each group with three points. A particular version of o3o3 is set as an example of many possibilities to construct LGM schemes on piecewise polynomial spaces in which the basis functions used are continuous at corner points and function spaces having continuous derivatives are shortly discussed. We propose a standard o3o3 scheme and a spectral o3o3 scheme as alternatives to the standard method of using the quadrature approximation. These two particular schemes selected were chosen for ease of implementation rather than optimal performance. In one dimension, compared to standard SEM3, o3o3 has a larger CFL condition benefiting from the use of a regular collocation grid. While SEM3 uses the irregular Legendre–Gauss–Lobatto collocation grid, o3o3 uses a regular grid. This is considered an advantage for physical parameterizations. The shortest resolved wave is marginally smaller than that with SEM3. In two dimensions, o3o3 is implemented on a sparse grid where only a part of the points on the underlying regular grid are used for forecasting.
Steppeler J, Li J, Fang F, et al., 2019, Test of a cubic spline interface for physical processes with a 1-D third-order spectral element model, Tellus Series A: Dynamic Meteorology and Oceanography, Vol: 71, Pages: 1-6, ISSN: 0280-6495
A common way to introduce physical processes into numerical models of the atmosphere is to call the parameterization at every grid point. This can lead to considerable errors. A simple 1-D example is proposed to illustrate that when a physical process occurs at one grid point only, a considerable sampling error may occur, with the result that only a fraction of the true impact of this process is seen. The interface to the physical parameterization in numerical weather prediction model using a third-order 1-D spectral element method (SEM3) model is investigated by homogeneous advection. In SEM3, the grid points, called principal nodes, are at boundaries of computational intervals and two more collocation points in the interior of each cell. This article argues that it is sufficient to do the physical parameterization for principal nodes only that creating the interior grid-point values of physics schemes by linear interpolation. This is called the spline interface method. A simple condensation model of water is taken as an example. Compared to the standard paramaterization, which computes the physical processes at every grid point, the spline interface method is more accurate and has a potential to save computer time. It turns out that the standard method creates a noisy wave which can easily be filtered by hyperviscosity. In the spline interface to the condensation physics, the condensation is done at every third grid point only. Third-order spline methods are used to represent the condensation at other points. The method using a smaller grid to compute condensation represented the condensation process more accurately and produced less of the computational noise. This version could be run without hyperviscosity, as no significant computational noise mode was generated by condensation. By doing physical processes only at every third grid point computer time may be saved.
Xiao D, Heaney CE, Fang F, et al., 2019, A domain decomposition non-intrusive reduced order model for turbulent flows, Computers and Fluids, Vol: 182, Pages: 15-27, ISSN: 0045-7930
In this paper, a new Domain Decomposition Non-Intrusive Reduced Order Model (DDNIROM) is developed for turbulent flows. The method works by partitioning the computational domain into a number of subdomains in such a way that the summation of weights associated with the finite element nodes within each subdomain is approximately equal, and the communication between subdomains is minimised. With suitably chosen weights, it is expected that there will be approximately equal accuracy associated with each subdomain. This accuracy is maximised by allowing the partitioning to occur through areas of the domain that have relatively little flow activity, which, in this case, is characterised by the pointwise maximum Reynolds stresses.A Gaussian Process Regression (GPR) machine learning method is used to construct a set of local approximation functions (hypersurfaces) for each subdomain. Each local hypersurface represents not only the fluid dynamics over the subdomain it belongs to, but also the interactions of the flow dynamics with the surrounding subdomains. Thus, in this way, the surrounding subdomains may be viewed as providing boundary conditions for the current subdomain.We consider a specific example of turbulent air flow within an urban neighbourhood at a test site in London and demonstrate the effectiveness of the proposed DDNIROM.
Yang P, Xiang J, Fang F, et al., 2019, A fidelity fluid-structure interaction model for vertical axis tidal turbines in turbulence flows, APPLIED ENERGY, Vol: 236, Pages: 465-477, ISSN: 0306-2619
Xiao D, Fang F, Pain C, et al., 2019, Machine learning-based rapid response tools for regional air pollution modelling, Atmospheric Environment, Vol: 199, Pages: 463-473, ISSN: 1352-2310
A parameterised non-intrusive reduced order model (P-NIROM) based on proper orthogonal decomposition (POD) and machine learning methods has been firstly developed for model reduction of pollutant transport equations. Our motivation is to provide rapid response urban air pollution predictions and controls. The varying parameters in the P-NIROM are pollutant sources. The training data sets are obtained from the high fidelity modelling solutions (called snapshots) for selected parameters (pollutant sources, here) over the parameter space . From these training data sets, the machine learning method is used to generate the relationship between the reduced solutions and inputs (pollutant sources) over . Furthermore a set of hyper-surface functions associated with each POD basis function is constructed for representing the fluid dynamics over the reduced space. The accuracy of the P-NIROM is highly dependent on the quality of the training set, here obtained from the high fidelity model. Over existing machine learning methods, the P-NIROM algorithm proposed here has the advantages that (1) it is combined with NIROM, thus providing rapid and reasonably accurate solutions; and (2) it is a robust and efficient approach for representation of any parametrised partial differential equations as the model parameters/inputs vary. In this study, we demonstrate the way how to implement the P-NIROM for the pollutant transport equation (but not limited to due to its robustness). Its predictive capability is illustrated in a three-dimensional (3-D) simulation of power plant plumes over a large region in China, where the varying parameters are the emission intensity at three locations. Results indicate that in comparison to the high fidelity model, the CPU cost is reduced by factor up to five orders of magnitude while reasonable accuracy remains.
Yang P, Xiang J, Fang F, et al., 2019, Modelling of fluid-structure interaction for moderate reynolds number flows using an immersed-body method, COMPUTERS & FLUIDS, Vol: 179, Pages: 613-631, ISSN: 0045-7930
Xiao D, Heaney CE, Mottet L, et al., 2019, A reduced order model for turbulent flows in the urban environment using machine learning, Building and Environment, Vol: 148, Pages: 323-337, ISSN: 0360-1323
To help create a comfortable and healthy indoor and outdoor environment in which to live, there is a need to understand turbulent air flows within the urban environment. To this end, building on a previously reported method [1], we develop a fast-running Non-Intrusive Reduced Order Model (NIROM) for predicting the turbulent air flows found within an urban environment. To resolve larger scale turbulent fluctuations, we employ a Large Eddy Simulation (LES) model and solve the resulting computational model on unstructured meshes. The objective is to construct a rapid-running NIROM from these results that will have ‘similar’ dynamics to the original LES model. Based on Proper Orthogonal Decomposition (POD) and machine learning techniques, this Reduced Order Model (ROM) is six orders of magnitude faster than the high-fidelity LES model and we demonstrate how ‘similar’ it can be to the high-fidelity model by comparing statistical quantities such as the mean flows, Reynolds stresses and probability densities of the velocities. We also include validation of the high-fidelity model against data from wind tunnel experiments.This paper represents a key step towards the use of reduced order modelling for operational purposes with the tantalising possibility of it being used in place of Gaussian plume models, and the potential for greatly improved model fidelity and confidence.
Hu R, Fang F, Salinas P, et al., 2019, Numerical simulation of floods from multiple sources using an adaptive anisotropic unstructured mesh method, Advances in Water Resources, Vol: 123, Pages: 173-188, ISSN: 0309-1708
The coincidence of two or more extreme events (precipitation and storm surge, for example) may lead to severe floods in coastal cities. It is important to develop powerful numerical tools for improved flooding predictions (especially over a wide range of spatial scales - metres to many kilometres) and assessment of joint influence of extreme events. Various numerical models have been developed to perform high-resolution flood simulations in urban areas. However, the use of high-resolution meshes across the whole computational domain may lead to a high computational burden. More recently, an adaptive isotropic unstructured mesh technique has been first introduced to urban flooding simulations and applied to a simple flooding event observed as a result of flow exceeding the capacity of the culvert during the period of prolonged or heavy rainfall. Over existing adaptive mesh refinement methods (AMR, locally nested static mesh methods), this adaptive unstructured mesh technique can dynamically modify (both, coarsening and refining the mesh) and adapt the mesh to achieve a desired precision, thus better capturing transient and complex flow dynamics as the flow evolves.In this work, the above adaptive mesh flooding model based on 2D shallow water equations (named as Floodity) has been further developed by introducing (1) an anisotropic dynamic mesh optimization technique (anisotropic-DMO); (2) multiple flooding sources (extreme rainfall and sea-level events); and (3) a unique combination of anisotropic-DMO and high-resolution Digital Terrain Model (DTM) data. It has been applied to a densely urbanized area within Greve, Denmark. Results from MIKE 21 FM are utilized to validate our model. To assess uncertainties in model predictions, sensitivity of flooding results to extreme sea levels, rainfall and mesh resolution has been undertaken. The use of anisotropic-DMO enables us to capture high resolution topographic features (buildings, rivers and streets) only where and when
Xiao D, Du J, Fang F, et al., 2018, Parameterised non-intrusive reduced order methods for ensemble Kalman filter data assimilation, Computers and Fluids, Vol: 177, Pages: 69-77, ISSN: 0045-7930
This paper presents a novel Ensemble Kalman Filter (EnKF) data assimilation method based on a parameterised non-intrusive reduced order model (P-NIROM) which is independent of the original computational code. EnKF techniques involve the expensive calculations of ensembles. In this work, the recently developed P-NIROM Xiao et al. [40] is incorporated into EnKF to speed up the ensemble simulations. A reduced order flow dynamical model is generated from the solution snapshots, which are obtained from a number of the high fidelity full simulations over the specific parametric space RP. The varying parameter is the background error covariance σ ∈ RP. Using the Smolyak sparse grid method, a set of parameters in the Gaussian probability density function is selected as the training points. The proposed method uses a two-level interpolation method for constructing the P-NIROM using a Radial Basis Function (RBF) interpolation method. The first level interpolation approach is used for generating the solution snapshots and POD basis functions for any given background error covariance while the second level interpolation approach for forming a set of hyper-surfaces representing the reduced system.The EnKF in combination with P-NIROM (P-NIROM-EnKF) has been implemented within an unstructured mesh finite element ocean model and applied to a three dimensional wind driven circulation gyre case. The numerical results show that the accuracy of ensembles and updated solutions using the P-NIROM-EnKF is maintained while the computational cost is significantly reduced by several orders of magnitude in comparison to the full-EnKF.
Li J, Zheng J, Zhu J, et al., 2018, Performance of Adaptive Unstructured Mesh Modelling in Idealized Advection Cases over Steep Terrains, ATMOSPHERE, Vol: 9, ISSN: 2073-4433
Xiao D, Fang F, Pain C, et al., 2018, Non-intrusive model reduction for a 3D unstructured mesh control volume finite element reservoir model and its application to fluvial channels, International Journal of Oil, Gas and Coal Technology, Vol: 19, Pages: 316-339, ISSN: 1753-3309
non-intrusive model reduction computational method using hypersurfaces representation has been developed for reservoir simulation and further applied to 3D fluvial channel problems in this work. This is achieved by a combination of a radial basis function (RBF) interpolation and proper orthogonal decomposition (POD) method. The advantage of the method is that it is generic and non-intrusive, that is, it does not require modifications to the original complex source code, for example, a 3D unstructured mesh control volume finite element (CVFEM) reservoir model used here. The capability of this non-intrusive reduced order model (NIROM) based on hypersurfaces representation has been numerically illustrated in a horizontally layered porous media case, and then further applied to a 3D complex fluvial channel case. By comparing the results of the NIROM against the solutions obtained from the high fidelity full model, it is shown that this NIROM results in a large reduction in the CPU computation cost while much of the details are captured.
Heaney C, Salinas P, Pain C, et al., 2018, Well Optimisation With Goal-Based Sensitivity Maps Using Time Windows And Ensemble Perturbations, European conference on mathematics of oil recovery
Yang L, Lyu Z, Yang P, et al., 2018, Numerical Simulation of Attenuator Wave Energy Converter using One-Fluid Formulation, Proceedings of the 28th International Ocean and Polar Engineering Conference
Song J, Fan S, Lin W, et al., 2018, Natural ventilation in cities: the implications of fluid mechanics, BUILDING RESEARCH AND INFORMATION, Vol: 46, Pages: 809-828, ISSN: 0961-3218
Hu R, Fang F, Salinas P, et al., 2018, Unstructured mesh adaptivity for urban flooding modelling, Journal of Hydrology
Heaney CE, Salinas P, Pain CC, et al., 2018, Well optimisation with goal-based sensitivity maps using time windows and ensemble perturbations
Knowledge of the sensitivity of a solution to small changes in the model parameters is exploited in many areas in computational physics and used to perform mesh adaptivity, or to correct errors based on discretisation and sub-grid-scale modelling errors, to perform the assimilation of data based on adjusting the most sensitive parameters to the model-observation misfit, and similarly to form optimised sub-grid-scale models. We present a goal-based approach for forming sensitivity (or importance) maps using ensembles. These maps are defined as regions in space and time of high relevance for a given goal, for example, the solution at an observation point within the domain. The presented approach relies solely on ensembles obtained from the forward model and thus can be used with complex models for which calculating an adjoint is not a practical option. This provides a simple approach for optimisation of sensor placement, goal based mesh adaptivity, assessment of goals and data assimilation. We investigate methods which reduce the number of ensembles used to construct the maps yet which retain reasonable fidelity of the maps. The fidelity comes from an integrated method including a goal-based approach, in which the most up-to-date importance maps are fed back into the perturbations to focus the algorithm on the key variables and domain areas. Also within the method smoothing is applied to the perturbations to obtain a multi-scale, global picture of the sensitivities; the perturbations are orthogonalised in order to generate a well-posed system which can be inverted; and time windows are applied (for time dependent problems) where we work backwards in time to obtain greater accuracy of the sensitivity maps. The approach is demonstrated on a multi-phase flow problem.
Zhang T, Fang F, Feng P, 2017, Simulation of dam/levee-break hydrodynamics with a three-dimensional implicit unstructured-mesh finite element model, ENVIRONMENTAL FLUID MECHANICS, Vol: 17, Pages: 959-979, ISSN: 1567-7419
Wang Z, Xiao D, Fang F, et al., 2017, Model identification of reduced order fluid dynamics systems using deep learning, International Journal for Numerical Methods in Fluids, Vol: 86, Pages: 255-268, ISSN: 0271-2091
This paper presents a novel model reduction method: deep learning reduced order model, which is based on proper orthogonal decomposition and deep learning methods. The deep learning approach is a recent technological advancement in the field of artificial neural networks. It has the advantage of learning the nonlinear system with multiple levels of representation and predicting data. In this work, the training data are obtained from high fidelity model solutions at selected time levels. The long short-term memory network is used to construct a set of hypersurfaces representing the reduced fluid dynamic system. The model reduction method developed here is independent of the source code of the full physical system.The reduced order model based on deep learning has been implemented within an unstructured mesh finite element fluid model. The performance of the new reduced order model is evaluated using 2 numerical examples: an ocean gyre and flow past a cylinder. These results illustrate that the CPU cost is reduced by several orders of magnitude whilst providing reasonable accuracy in predictive numerical modelling.
Xiao D, Fang F, Pain C, et al., 2017, Towards non-intrusive reduced order 3D free surface flow modelling, Ocean Engineering, Vol: 140, Pages: 155-168, ISSN: 1873-5258
In this article, we describe a novel non-intrusive reduction model for three-dimensional (3D) free surface flows. However, in this work we limit the vertical resolution to be a single element. So, although it does resolve some non-hydrostatic effects, it does not examine the application of reduced modelling to full 3D free surface flows, but it is an important step towards 3D modelling. A newly developed non-intrusive reduced order model (NIROM) (Xiao et al., 2015a) has been used in this work. Rather than taking the standard POD approach using the Galerkin projection, a Smolyak sparse grid interpolation method is employed to generate the NIROM. A set of interpolation functions is constructed to calculate the POD coefficients, where the POD coefficients at previous time steps are the inputs of the interpolation function. Therefore, this model is non-intrusive and does not require modifications to the code of the full system and is easy to implement.By using this new NIROM, we have developed a robust and efficient reduced order model for free surface flows within a 3D unstructured mesh finite element ocean model. What distinguishes the reduced order model developed here from other existing reduced order ocean models is (1) the inclusion of 3D dynamics with a free surface (the 3D computational domain and meshes are changed with the movement of the free surface); (2) the incorporation of wetting-drying; and (3) the first implementation of non-intrusive reduced order method in ocean modelling. Most importantly, the change of the computational domain with the free surface movement is taken into account in reduced order modelling. The accuracy and predictive capability of the new non-intrusive free surface flow ROM have been evaluated in Balzano and Okushiri tsunami test cases. This is the first step towards 3D reduced order modelling in realistic ocean cases. Results obtained show that the accuracy of free surface problems relative to the high fidelity model is maintained
Xiao D, Fang F, Pain C, et al., 2017, A parameterized non-intrusive reduced order model anderror analysis for general time-dependent nonlinear partialdifferential equations and its applications, Computer Methods in Applied Mechanics and Engineering, Vol: 317, Pages: 868-889, ISSN: 0045-7825
A novel parameterized non-intrusive reduced order model (P-NIROM) based onproper orthogonal decomposition (POD) has been developed.This P-NIROM is ageneric and efficient approach for model reduction of parameterized partial differen-tial equations (P-PDEs). Over existing parameterized reduced order models (P-ROM)(most of them are based on the reduced basis method), it is non-intrusive and inde-pendent on partial differential equations and computational codes. During the trainingprocess, the Smolyak sparse grid method is used to select a set of parameters over aspecific parameterized space (Ωp∈ RP). For each selected parameter, the reduced ba-sis functions are generated from the snapshots derived froma run of the high fidelitymodel. More generally, the snapshots and basis function sets for any parameters overΩpcan be obtained using an interpolation method. The P-NIROM can then be con-structed by using our recently developed technique [50,53] where either the Smolyakor radial basis function (RBF) methods are used to generate aset of hyper-surfacesrepresenting the underlying dynamical system over the reduced space.The new P-NIROM technique has been applied to parameterizedNavier-Stokesequations and implemented with an unstructured mesh finite element model. The ca-pability of this P-NIROM has been illustrated numerically by two test cases: flow pasta cylinder and lock exchange case. The prediction capabilities of the P-NIROM havebeen evaluated by varying the viscosity, initial and boundary conditions. The resultsshow that this P-NIROM has captured the quasi-totality of the details of the flow withCPU speedup of three orders of magnitude. An error analysis for the P-NIROM hasbeen carried out.
Yang P, Xiang J, Chen M, et al., 2016, The immersed-body gas-solid interaction model for blast analysis in fractured solid media, International Journal of Rock Mechanics and Mining Sciences, Vol: 91, Pages: 119-132, ISSN: 1873-4545
Blast-induced fractures are simulated by a novel gas-solid interaction model, which combines an immersed-body method and a cohesive zone fracture model. The approach employs a finite element fluid model and a combined finite-discrete element solid model. This model is fully coupled and simulates the whole blasting process including gas pressure impulse, shock wave propagation, gas expansion, fragmentation and burden movement phases. In the fluid model, the John-Wilkins-Lee equation of state is introduced to resolve the relationship between pressure and density of the highly compressible gas in blasts and explosions. A Q-scheme is used to stabilise the model when solving extremely high pressure situations. Two benchmark tests, blasting cylinder and projectile fire, are used to validate this coupled model. The results of these tests are in good agreement with experimental data. To demonstrate the potential of the proposed method, a blasting engineering simulation with shock waves, fracture propagation, gas-solid interaction and flying fragments is simulated.
Xiao D, Yang P, Fang F, et al., 2016, A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting, Journal of Computational Physics, Vol: 330, Pages: 221-224, ISSN: 0021-9991
This work presents the first application of a non-intrusive reduced order method to model solid interacting with compressible fluid flows to simulate crack initiation and propagation. In the high fidelity model, the coupling process is achieved by introducing a source term into the momentum equation, which represents the effects of forces of the solid on the fluid. A combined single and smeared crack model with the Mohr–Coulomb failure criterion is used to simulate crack initiation and propagation. The non-intrusive reduced order method is then applied to compressible fluid and fractured solid coupled modelling where the computational cost involved in the full high fidelity simulation is high. The non-intrusive reduced order model (NIROM) developed here is constructed through proper orthogonal decomposition (POD) and a radial basis function (RBF) multi-dimensional interpolation method.The performance of the NIROM for solid interacting with compressible fluid flows, in the presence of fracture models, is illustrated by two complex test cases: an immersed wall in a fluid and a blasting test case. The numerical simulation results show that the NIROM is capable of capturing the details of compressible fluids and fractured solids while the CPU time is reduced by several orders of magnitude. In addition, the issue of whether or not to subtract the mean from the snapshots before applying POD is discussed in this paper. It is shown that solutions of the NIROM, without mean subtracted before constructing the POD basis, captured more details than the NIROM with mean subtracted from snapshots.
Fang F, Pain C, Navon I, et al., 2016, An efficient goal based reduced order model approach for targeted adaptive observations, International Journal for Numerical Methods in Fluids, Vol: 83, Pages: 263-275, ISSN: 0271-2091
An efficient adjoint sensitivity technique for optimally collecting targeted observations is presented. The targeting technique incorporates dynamical information from the numerical model predictions to identify when, where, and what types of observations would provide the greatest improvement to specific model forecasts at a future time. A functional (goal) is defined to measure what is considered important in modelling problems. The adjoint sensitivity technique is used to identify the impact of observations on the predictive accuracy of the functional, then placing the sensors at the locations with high impacts. The adaptive (goal) observation technique developed here has the following features: (1) over existing targeted observation techniques, its novelty lies in that the interpolation error of numerical results is introduced to the functional (goal) which ensures the measurements are a distance apart; (2) the use of proper orthogonal decomposition (POD) and reduced order modeling (ROM) for both the forward and backward simulations, thus reducing the computational cost; and (3) the use of unstructured meshes. The targeted adaptive observation technique, is developed here within an unstructured mesh finite element model (Fluidity). In this work, a POD ROM is used to form the reduced order forward model by projecting the original complex model from a high dimensional space onto a reduced order space. The reduced order adjoint model is then constructed directly from the reduced order forward model. This efficient adaptive observation technique has been validated with two test cases: a model of an ocean Gyre and a model of 2D urban street canyon flows.
Lin Z, Xiao D, Fang F, et al., 2016, Non-intrusive reduced order modelling with least squares fitting on a sparse grid, International Journal for Numerical Methods in Fluids, Vol: 83, Pages: 291-306, ISSN: 0271-2091
This article presents a non-intrusive reduced order model (NIROM) for general, dynamic partial differential equations. Based upon proper orthogonal decomposition (POD) and Smolyak sparse grid collocation, the method first projects the unknowns with full space and time coordinates onto a reduced POD basis. Then we introduce a new least squares fitting procedure to approximate the dynamical transition of the POD coefficients between subsequent time steps taking only a set of full model solution snapshots as the training data during the construction. Thus, neither the physical details nor further numerical simulations of the original PDE model is required by this methodology and the level of non-intrusiveness is improved compared to existing ROMs. Furthermore, we take adaptive measures to address the instability issue arising from reduced order iterations of the POD coefficients.This model can be applied to a wide range of physical and engineering scenarios and we test it on a couple problems in fluid dynamics. It is demonstrated that this reduced order approach captures the dominant features of the high fidelity models with reasonable accuracy while the computation complexity is reduced by several orders of magnitude.
Xiao D, fang F, pain C, et al., 2016, Non-intrusive Reduced Order Modelling of Waterflooding in Geologically Heterogeneous Reservoirs, ECMOR XV - 15th European Conference on the Mathematics of Oil Recovery
Xiao D, Lin Z, Fang F, et al., 2016, Non-intrusive reduced order modeling for multiphase porous media flows using smolyak sparse grids, International Journal for Numerical Methods in Fluids, Vol: 83, Pages: 205-219, ISSN: 0271-2091
In this article, we describe a non-intrusive reduction method for porous media multiphase flows using Smolyak sparse grids. This is the first attempt at applying such an non-intrusive reduced-order modelling (NIROM) based on Smolyak sparse grids to porous media multiphase flows. The advantage of this NIROM for porous media multiphase flows resides in that its non-intrusiveness, which means it does not require modifications to the source code of full model. Another novelty is that it uses Smolyak sparse grids to construct a set of hypersurfaces representing the reduced-porous media multiphase problem. This NIROM is implemented under the framework of an unstructured mesh control volume finite element multiphase model. Numerical examples show that the NIROM accuracy relative to the high-fidelity model is maintained, whilst the computational cost is reduced by several orders of magnitude.
Adam A, Pavlidis D, Percival J, et al., 2016, Higher-order conservative interpolation between control-volume meshes: Application to advection and multiphase flow problems with dynamic mesh adaptivity, Journal of Computational Physics, Vol: 321, Pages: 512-531, ISSN: 1090-2716
A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach.
du J, Zhu J, Fang F, et al., 2016, Ensemble data assimilation applied to an adaptive mesh ocean model, International Journal for Numerical Methods in Fluids, Vol: 82, Pages: 997-1009, ISSN: 0271-2091
In this study, a first attempt has been made to introduce mesh adaptivity into the ensemble Kalman fiter (EnKF) method. The EnKF data assimilation system was established for an unstructured adaptive mesh ocean model (Fluidity, Imperial College London). The mesh adaptivity involved using high resolution mesh at the regions of large flow gradients and around the observation points in order to reduce the representativeness errors of the observations. The use of adaptive meshes unavoidably introduces difficulties in the implementation of EnKF. The ensembles are defined at different meshes. To overcome the difficulties, a supermesh technique is employed for generating a reference mesh. The ensembles are then interpolated from their own mesh onto the reference mesh. The performance of the new EnKF data assimilation system has been tested in the Munk gyre flow test case. The discussion of this paper will focus on (a) the development of the EnKF data assimilation system within an adaptive mesh model and (b) the advantages of mesh adaptivity in the ocean data assimilation model.
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