Developments of entropy-stable residual distribution methods for conservation laws I: Scalar problems

Ismail, Farzad; Chizari, Hossain

doi:10.1016/j.jcp.2016.10.065

Cited by 20 publications

(1 citation statement)

References 34 publications

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“…In order to reach the full potential of RD method, Ismail and Chizari [13] have developed a new class of RD method called Flux-Difference approach which ensures automatic conservation of the primary variables without any dependence on cell-averaging for any well-posed equations and preserves the spatial second-order accuracy on unsteady problems using any consistent explicit time integration scheme. However, since these flux-difference RD methods are new, very little has been done to understand the inherent properties of the scheme.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Grid Skewness on Non-Unified Compact Residual Distribution Methods for Scalar Advection Diffusion Problems

Aminnuddin¹,

Ismail²,

Mohamed³

et al. 2020

CFDL

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In this paper, the newly developed residual distribution (RD) method called the Flux-Difference approach is combined with the Galerkin method to solve the advectiondiffusion equation in separate (non-unified) manner. It is due to the incapability of variation grid skewness in finite volume. This Flux-Difference RD method maintains a compact stencil and the whole process of solving advection-diffusion do not require additional equations. In order to improve the order of accuracy losses by the classic RD schemes, the present scheme will be tested using non-unified manners. The numerical results show that the Flux-Difference RD method preserves second-order accuracy up to about skewness 0.4 but drops to about 1.5 orders accurate when grid skewness is 0.6.

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Section: Introductionmentioning

confidence: 99%