7 results found
Mengaldo G, De Grazia D, Vincent PE, et al., 2015, On the connections between discontinuous Galerkin and flux reconstruction schemes: extension to curvilinear meshes, Journal of Scientific Computing, Vol: 67, Pages: 1272-1292, ISSN: 1573-7691
This paper investigates the connections between many popular variants of the well-established discontinuous Galerkin method and the recently developed high-order flux reconstruction approach on irregular tensor-product grids. We explore these connections by analysing three nodal versions of tensor-product discontinuous Galerkin spectral element approximations and three types of flux reconstruction schemes for solving systems of conservation laws on irregular tensor-product meshes. We demonstrate that the existing connections established on regular grids are also valid on deformed and curved meshes for both linear and nonlinear problems, provided that the metric terms are accounted for appropriately. We also find that the aliasing issues arising from nonlinearities either due to a deformed/curved elements or due to the nonlinearity of the equations are equivalent and can be addressed using the same strategies both in the discontinuous Galerkin method and in the flux reconstruction approach. In particular, we show that the discontinuous Galerkin and the flux reconstruction approach are equivalent also when using higher-order quadrature rules that are commonly employed in the context of over- or consistent-integration-based dealiasing methods. The connections found in this work help to complete the picture regarding the relations between these two numerical approaches and show the possibility of using over- or consistent-integration in an equivalent manner for both the approaches.
Mengaldo G, De Grazia D, Moxey D, et al., 2015, Dealiasing techniques for high-order spectral element methods on regular and irregular grids, Journal of Computational Physics, Vol: 299, Pages: 56-81, ISSN: 0021-9991
High-order methods are becoming increasingly attractive in both academia and industry, especially in the context of computational fluid dynamics. However, before they can be more widely adopted, issues such as lack of robustness in terms of numerical stability need to be addressed, particularly when treating industrial-type problems where challenging geometries and a wide range of physical scales, typically due to high Reynolds numbers, need to be taken into account. One source of instability is aliasing effects which arise from the nonlinearity of the underlying problem. In this work we detail two dealiasing strategies based on the concept of consistent integration. The first uses a localised approach, which is useful when the nonlinearities only arise in parts of the problem. The second is based on the more traditional approach of using a higher quadrature. The main goal of both dealiasing techniques is to improve the robustness of high order spectral element methods, thereby reducing aliasing-driven instabilities. We demonstrate how these two strategies can be effectively applied to both continuous and discontinuous discretisations, where, in the latter, both volumetric and interface approximations must be considered. We show the key features of each dealiasing technique applied to the scalar conservation law with numerical examples and we highlight the main differences in terms of implementation between continuous and discontinuous spatial discretisations.
Cantwell CD, Moxey D, Comerford A, et al., 2015, Nektar++: an open-source spectral/hp element framework, Computer Physics Communications, Vol: 192, Pages: 205-219, ISSN: 0010-4655
Nektar++ is an open-source software framework designed to support the development of high-performance scalable solvers for partial differential equations using the spectral/hphp element method. High-order methods are gaining prominence in several engineering and biomedical applications due to their improved accuracy over low-order techniques at reduced computational cost for a given number of degrees of freedom. However, their proliferation is often limited by their complexity, which makes these methods challenging to implement and use. Nektar++ is an initiative to overcome this limitation by encapsulating the mathematical complexities of the underlying method within an efficient C++ framework, making the techniques more accessible to the broader scientific and industrial communities. The software supports a variety of discretisation techniques and implementation strategies, supporting methods research as well as application-focused computation, and the multi-layered structure of the framework allows the user to embrace as much or as little of the complexity as they need. The libraries capture the mathematical constructs of spectral/hphp element methods, while the associated collection of pre-written PDE solvers provides out-of-the-box application-level functionality and a template for users who wish to develop solutions for addressing questions in their own scientific domains.
Mengaldo G, Kravtsova M, Ruban A, et al., 2015, Triple-deck and direct numerical simulation analyses high-speed subsonic flows past a roughness element, Journal of Fluid Mechanics, Vol: 774, Pages: 311-323, ISSN: 1469-7645
This paper is concerned with the boundary-layer separation in subsonic and transonic flows caused by a two-dimensional isolated wall roughness. The process of the separation is analysed by means of two approaches: the direct numerical simulation (DNS) of the flow using the Navier–Stokes equations, and the numerical solution of the triple-deck equations. Since the triple-deck theory relies on the assumption that the Reynolds number ( ) is large, we performed the Navier–Stokes calculations at Re = 4 x 10^5 based on the distance of the roughness element from the leading edge of the flat plate. This Re is also relevant for aeronautical applications. Two sets of calculation were conducted with the free-stream Mach number Ma_∞ = 0.5 and Ma_∞ = 0.87 . We used different roughness element heights, some of which were large enough to cause a well-developed separation region behind the roughness. We found that the two approaches generally compare well with one another in terms of wall shear stress, longitudinal pressure gradient and detachment/reattachment points of the separation bubbles (when present). The main differences were found in proximity to the centre of the roughness element, where the wall shear stress and longitudinal pressure gradient predicted by the triple-deck theory are noticeably different from those predicted by DNS. In addition, DNS predicts slightly longer separation regions.
De Grazia D, Mengaldo G, Moxey D, et al., 2014, Connections between the discontinuous Galerkin method and high-order flux reconstruction schemes, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Vol: 75, Pages: 860-877, ISSN: 0271-2091
Mengaldo G, Tricerri P, Crosetto P, et al., 2012, A comparative study of different nonlinear hyperelastic isotropic arterial wall models in patient-specific vascular flow simulations in the aortic arch, MOX website, Publisher: MOX
Blood flow in major arteries gives rise to a complex fluid-structure interaction (FSI) problem. The mechanical behaviour of the tissues composing the vessel wall is highly nonlinear. However, when the wall deformation is small it can be argued that the effect of the non-linearities to the flow field is small and indeed several authors employ a linear constitutive law. In the aortic arch, however, the deformations experienced by the vessel wall during the heart beat are substantial. In this work we have implemented different non-linear constitutive relations for the vessel wall. We compare the flow field and related quantities such as wall shear stress obtained on an anatomically realistic geometry of aortic arch reconstructed from clinical images and using physiological data. Particular attention is also devoted to the efficiency of the algorithms employed. The fluid-structure interaction problem is solved with a fully coupled approach and using the exact Jacobians for each different structural model to guarantee a second order convergence of the Newton method.
Mengaldo G, Moro V, Rossettini L, et al., 2008, Moon Orbiter, Propulsion Issues, Joint Annual Meeting of LEAG-ICEUM-SRR
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