Addressing the Challenges of Implementation of High-Order Finite-Volume Schemes for Atmospheric Dynamics on Unstructured Meshes

Tsoutsanis, Panagiotis; Drikakis, Dimitris

doi:10.7712/100016.1846.8406

Cited by 10 publications

(6 citation statements)

References 52 publications

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“…To avoid the growth of instabilities in the numerical solution, we may add a small artificial viscosity. However, as already discussed in [102,103,105], this leads to a smoothness of the boundary of the bubble, that is affected by numerical dissipation. Figure 12 shows the results obtained at time instants t ∈ {600, 700, 800, 900}s using a constant artificial viscosity with µ = 10 −6 and a very coarse primal mesh composed of only 5172 triangles.…”

Section: Warm Bubble In Two Space Dimensionsmentioning

confidence: 88%

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Efficient high order accurate staggered semi-implicit discontinuous Galerkin methods for natural convection problems

et al. 2020

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In this article we propose a new family of high order staggered semi-implicit discontinuous Galerkin (DG) methods for the simulation of natural convection problems. Assuming small temperature fluctuations, the Boussinesq approximation is valid and in this case the flow can simply be modeled by the incompressible Navier-Stokes equations coupled with a transport equation for the temperature and a buoyancy source term in the momentum equation. Our numerical scheme is developed starting from the work presented in [1,2,3], in which the spatial domain is discretized using a face-based staggered unstructured mesh. The pressure and temperature variables are defined on the primal simplex elements, while the velocity is assigned to the dual grid. For the computation of the advection and diffusion terms, two different algorithms are presented: i) a purely Eulerian explicit upwind-type scheme and ii) a semi-Lagrangian approach. The first methodology leads to a conservative scheme whose major drawback is the time step restriction imposed by the CFL stability condition due to the explicit discretization of the convective terms. On the contrary, computational efficiency can be notably improved relying on a semi-Lagrangian approach in which the Lagrangian trajectories of the flow are tracked back. This method leads to an unconditionally stable scheme if the diffusive terms are discretized implicitly. Once the advection and diffusion contributions have been computed, the pressure Poisson equation is solved and the velocity is updated. As a second model for the computation of buoyancy-driven flows, in this paper we also consider the full compressible Navier-Stokes equations. The staggered semi-implicit DG method first proposed in [4] for all Mach number flows is properly extended to account for the gravity source terms arising in the momentum and energy conservation laws. In order to assess the validity and the robustness of our novel class of staggered semi-implicit DG schemes, several classical benchmark problems are considered, showing in all cases a good agreement with available numerical reference data. Furthermore, a detailed comparison between the incompressible and the compressible solver is presented. Finally, advantages and disadvantages of the Eulerian and the semi-Lagrangian methods for the discretization of the nonlinear convective terms are carefully studied.

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Section: Warm Bubble In Two Space Dimensionsmentioning

confidence: 88%

“…We now extend the warm bubble test to a three-dimensional domain, following the setup described in [105,104]. To this end, we define the computational domain Ω = [0, 1] × [0, 1] × [0, 1.5] km.…”

Section: Warm Bubble In Three Space Dimensionsmentioning

confidence: 99%

Efficient high order accurate staggered semi-implicit discontinuous Galerkin methods for natural convection problems

et al. 2020

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“…The present polynomial reconstruction is based upon the approaches of [53,63], that have been applied to smooth and discontinuous flow problems [2][3][4][5]20,46,49,50,57,[59][60][61][62][64][65][66][67], and only the key-components will be presented herein and the reader is referred to [53,63] for further details. For the reconstruction, a transformation from physical space to a reference space as introduced by Dumbser et al [16,17] is employed to reduce the scaling effects that occur at unstructured meshes consisting of elements of different shape and size.…”

Section: Reconstructionmentioning

confidence: 99%

CWENO Finite-Volume Interface Capturing Schemes for Multicomponent Flows Using Unstructured Meshes

et al. 2021

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In this paper we extend the application of unstructured high-order finite-volume central-weighted essentially non-oscillatory (CWENO) schemes to multicomponent flows using the interface capturing paradigm. The developed method achieves high-order accurate solution in smooth regions, while providing oscillation free solutions at discontinuous regions. The schemes are inherently compact in the sense that the central stencils employed are as compact as possible, and that the directional stencils are reduced in size, therefore simplifying their implementation. Several parameters that influence the performance of the schemes are investigated, such as reconstruction variables and their reconstruction order. The performance of the schemes is assessed under a series of stringent test problems consisting of various combinations of gases and liquids, and compared against analytical solutions, computational and experimental results available in the literature. The results obtained demonstrate the robustness of the new schemes for several applications, as well as their limitations within the present interface-capturing implementation.

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“…The reconstruction algorithm used is based upon the approaches [2,3,11,35], that have been applied to smooth and discontinuous flow problems [22,[38][39][40][41][42][43][44][45][46][47] and only key-components will be presented herein, since the focus is towards the stencil selection algorithms and the reader is referred to [2,3,35] for further details.…”

Section: Spatial Discretisationmentioning

confidence: 99%

Stencil selection algorithms for WENO schemes on unstructured meshes

Tsoutsanis

2023

Journal of Computational Physics

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In this paper, a family of stencil selection algorithms is presented for WENO schemes on unstructured meshes. The associated freedom of stencil selection for unstructured meshes, in the context of WENO schemes present a plethora of various stencil selection algorithms. The particular focus of this paper is to assess the performance of various stencil selection algorithm, investigate the parameters that dictate their robustness, accuracy and computational efficiency. Ultimately, efficient and robust stencils are pursued that can provide significant savings in computational performance, while retaining the nonoscillatory character of WENO schemes. This is achieved when making the stencil selection algorithms adaptive, based on the quality of the cells for unstructured meshes, that can in turn reduce the computational cost of WENO schemes. For assessing the performance of the developed algorithms well established test problems are employed. These include the least square approximation of polynomial functions, linear advection equation of smooth functions and solid body rotation test problem. Euler and Navier-Stokes equations test problems are also pursued such as the Shu-Osher test problem, the Double Mach Reflection, the supersonic Forward Facing step, the Kelvin-Helmholtz instability, the Taylor-Green Vortex, and the flow past a transonic circular cylinder. Crown

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Addressing the Challenges of Implementation of High-Order Finite-Volume Schemes for Atmospheric Dynamics on Unstructured Meshes

Abstract: Abstract. The solution of the non-hydrostatic compressible Euler equations using Weighted Es

Cited by 10 publications

References 52 publications

Efficient high order accurate staggered semi-implicit discontinuous Galerkin methods for natural convection problems

Efficient high order accurate staggered semi-implicit discontinuous Galerkin methods for natural convection problems

CWENO Finite-Volume Interface Capturing Schemes for Multicomponent Flows Using Unstructured Meshes

Stencil selection algorithms for WENO schemes on unstructured meshes

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