scholarly journals Efficient Implementation of High Order Reconstruction in Finite Volume Methods

2011 ◽  
pp. 553-560 ◽  
Author(s):  
Florian Haider ◽  
Pierre Brenner ◽  
Bernard Courbet ◽  
Jean-Pierre Croisille
Keyword(s):  
Finite Volume ◽  
Finite Volume Methods ◽  
Efficient Implementation ◽  
High Order ◽  
Order Reconstruction ◽  
High Order Reconstruction

Comparison of Fifth-Order WENO Scheme and Finite Volume WENO-Gas-Kinetic Scheme for Inviscid and Viscous Flow Simulation

2013 ◽  
Vol 14 (3) ◽  
pp. 599-620 ◽  
Author(s):  
Jun Luo ◽  
Lijun Xuan ◽  
Kun Xu
Keyword(s):  
Finite Volume ◽  
Control Volume ◽  
High Order ◽  
Gas Evolution ◽  
Weno Reconstruction ◽  
Flux Function ◽  
High Order Schemes ◽  
Order Reconstruction ◽  
High Order Reconstruction ◽  
Fifth Order

AbstractThe development of high-order schemes has been mostly concentrated on the limiters and high-order reconstruction techniques. In this paper, the effect of the flux functions on the performance of high-order schemes will be studied. Based on the same WENO reconstruction, two schemes with different flux functions, i.e., the fifth-order WENO method and the WENO-Gas-kinetic scheme (WENO-GKS), will be compared. The fifth-order finite difference WENO-SW scheme is a characteristic variable reconstruction based method which uses the Steger-Warming flux splitting for inviscid terms, the sixth-order central difference for viscous terms, and three stages Runge-Kutta time stepping for the time integration. On the other hand, the finite volume WENO-GKS is a conservative variable reconstruction based method with the same WENO reconstruction. But, it evaluates a time dependent gas distribution function along a cell interface, and updates the flow variables inside each control volume by integrating the flux function along the boundary of the control volume in both space and time. In order to validate the robustness and accuracy of the schemes, both methods are tested under a wide range of flow conditions: vortex propagation, Mach 3 step problem, and the cavity flow at Reynolds number 3200. Our study shows that both WENO-SW and WENO-GKS yield quantitatively similar results and agree with each other very well provided a sufficient grid resolution is used. With the reduction of mesh points, the WENO-GKS behaves to have less numerical dissipation and present more accurate solutions than those from the WENO-SW in all test cases. For the Navier-Stokes equations, since the WENO-GKS couples inviscid and viscous terms in a single flux evaluation, and the WENO-SW uses an operator splitting technique, it appears that the WENO-SW is more sensitive to the WENO reconstruction and boundary treatment. In terms of efficiency, the finite volume WENO-GKS is about 4 times slower than the finite differenceWENO-SW in two dimensional simulations. The current study clearly shows that besides high-order reconstruction, an accurate gas evolution model or flux function in a high-order scheme is also important in the capturing of physical solutions. In a physical flow, the transport, stress deformation, heat conduction, and viscous heating are all coupled in a single gas evolution process. Therefore, it is preferred to develop such a scheme with multi-dimensionality, and unified treatment of inviscid and dissipative terms. A high-order scheme does prefer a high-order gas evolution model. Even with the rapid advances of high-order reconstruction techniques, the first-order dynamics of the Riemann solution becomes the bottleneck for the further development of high-order schemes. In order to avoid the weakness of the low order flux function, the development of high-order schemes relies heavily on the weak solution of the original governing equations for the update of additional degree of freedom, such as the non-conservative gradients of flow variables, which cannot be physically valid in discontinuous regions.

High Order Finite Volume Methods Applied to Sediment Transport and Submarine Avalanches

2008 ◽  
pp. 247-258 ◽  
Author(s):  
D. Bresch ◽  
M. J. C. Díaz ◽  
E. D. Fernández-Nieto ◽  
A. M. Ferreiro ◽  
A. Mangeney
Keyword(s):  
Sediment Transport ◽  
Finite Volume ◽  
Finite Volume Methods ◽  
High Order

An improved Roe solver for high order reconstruction schemes

2020 ◽  
Vol 207 ◽  
pp. 104591 ◽  
Author(s):  
Omer Musa ◽  
Guoping Huang ◽  
Zonghan Yu ◽  
Qian Li
Keyword(s):  
High Order ◽  
Order Reconstruction ◽  
High Order Reconstruction ◽  
Roe Solver

Comparison of advection schemes for high-order h–p finite element and finite volume methods

2005 ◽  
Vol 10 (1-2) ◽  
pp. 233-252 ◽  
Author(s):  
M. Iskandarani ◽  
J.C. Levin ◽  
B.-J. Choi ◽  
D.B. Haidvogel
Keyword(s):  
Finite Element ◽  
Finite Volume ◽  
Finite Volume Methods ◽  
High Order ◽  
Advection Schemes
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