Publications
5 results found
Yamazaki H, Shipton J, Cullen MJP, et al., 2017, Vertical slice modelling of nonlinear Eady waves using a compatible finite element method, Journal of Computational Physics, Vol: 343, Pages: 130-149, ISSN: 1090-2716
A vertical slice model is developed for the Euler–Boussinesq equations with a constant temperature gradient in the direction normal to the slice (the Eady–Boussinesq model). The model is a solution of the full three-dimensional equations with no variation normal to the slice, which is an idealised problem used to study the formation and subsequent evolution of weather fronts. A compatible finite element method is used to discretise the governing equations. To extend the Charney–Phillips grid staggering in the compatible finite element framework, we use the same node locations for buoyancy as the vertical part of velocity and apply a transport scheme for a partially continuous finite element space. For the time discretisation, we solve the semi-implicit equations together with an explicit strong-stability-preserving Runge–Kutta scheme to all of the advection terms. The model reproduces several quasi-periodic lifecycles of fronts despite the presence of strong discontinuities. An asymptotic limit analysis based on the semi-geostrophic theory shows that the model solutions are converging to a solution in cross-front geostrophic balance. The results are consistent with the previous results using finite difference methods, indicating that the compatible finite element method is performing as well as finite difference methods for this test problem. We observe dissipation of kinetic energy of the cross-front velocity in the model due to the lack of resolution at the fronts, even though the energy loss is not likely to account for the large gap on the strength of the fronts between the model result and the semi-geostrophic limit solution.
Yamazaki H, Satomura T, Nikiforakis N, 2016, Three-dimensional cut-cell modelling for high-resolution atmospheric simulations, Quarterly Journal of the Royal Meteorological Society, Vol: 142, Pages: 1335-1350, ISSN: 1477-870X
Owing to the recent rapid development of computer technology, the resolution of atmospheric numerical models has increased substantially. With the use of next-generation supercomputers, atmospheric simulations using horizontal grid intervals of O(100)m or less will gain popularity. At such high resolution, more of the steep gradients in mountainous terrain will be resolved, which may result in large truncation errors in those models using terrain-following coordinates. In this study, a new three-dimensional (3D) Cartesian coordinate non-hydrostatic atmospheric model is developed. A cut-cell representation of topography based on finite-volume discretization is combined with a cell-merging approach, in which small cut cells are merged with neighbouring cells either vertically or horizontally. In addition, a block-structured mesh-refinement technique is introduced to achieve a variable resolution on the model grid, with the finest resolution occurring close to the terrain surface. The model successfully reproduces a flow over a 3D bell-shaped hill that shows a good agreement with the flow predicted by the linear theory. The ability of the model to simulate flows over steep terrain is demonstrated using a hemisphere-shaped hill. The advantage of a locally refined grid around the hill, with cut cells at the terrain surface, is also demonstrated. The model reproduces smooth mountain waves propagating over varying grid resolution without introducing large errors associated with the change of mesh resolution. At the same time, the model shows a good scalability on the locally refined grid.
Yamazaki H, Satomura T, 2012, Non‐hydrostatic atmospheric cut cell model on a block‐structured mesh, Atmospheric Science Letters, Vol: 13, Pages: 29-35, ISSN: 1530-261X
<jats:title>Abstract</jats:title><jats:p>A block‐structured Cartesian mesh approach based on the Building‐Cube Method is implemented into a 2D non‐hydrostatic atmospheric cut cell model to obtain high near‐ground resolution using Cartesian coordinates. A simple flux‐matching algorithm is introduced that ensures mass conservation across varying grid resolutions in a subcycling time integration. Results of simple diffusion and advection problems show that the method produces sufficiently accurate results with high computational efficiency. The developed model successfully reproduces a flow over a semicircular mountain on a locally refined mesh around the mountain. The result agrees well with that using a uniformly fine mesh. Copyright © 2011 Royal Meteorological Society</jats:p>
Yamazaki H, Satomura T, 2010, Nonhydrostatic Atmospheric Modeling Using a Combined Cartesian Grid, Monthly Weather Review, Vol: 138, Pages: 3932-3945, ISSN: 0027-0644
<jats:title>Abstract</jats:title> <jats:p>A new method for representing topography on a Cartesian grid is applied to a two-dimensional nonhydrostatic atmospheric model to achieve highly precise simulations over steep terrain. The shaved cell method based on finite-volume discretization is used along with a cell-combining approach in which small cut cells are combined with neighboring cells either vertically or horizontally. A unique staggered arrangement of variables enables quite simple computations of momentum equations by avoiding the evaluation of surface pressure and reducing the computational cost of combining cells for the velocity variables. The method successfully reproduces flows over a wide range of slopes, including steep slopes where significant errors are observed in a model using conventional terrain-following coordinates. The advantage of horizontal cell combination on extremely steep slopes is also demonstrated.</jats:p>
Yamazaki H, Satomura T, 2008, Vertically combined shaved cell method in a <b><i>z</i></b>‐coordinate nonhydrostatic atmospheric model, Atmospheric Science Letters, Vol: 9, Pages: 171-175, ISSN: 1530-261X
<jats:title>Abstract</jats:title><jats:p>The vertically combined shaved cell method is implemented into a <jats:italic>z</jats:italic>‐coordinate nonhydrostatic two‐dimensional atmospheric model based on the finite‐volume method. Quasi‐flux form fully compressible equations are employed as governing equations. The results of flow over a bell‐shaped mountain and a semicircular mountain are compared to those from a model using terrain‐following coordinates. These results indicate that the proposed method does not suffer from vertical velocity errors at the edge of the cells, and reproduces smooth and accurate mountain waves over not only gentle but also steep slopes where significant errors are observed in the terrain‐following model. Copyright © 2008 Royal Meteorological Society</jats:p>
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