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

Assessment of WENO and SFV High-Order Reconstruction Schemes for Aerodynamic Flows

2013 ◽  
Author(s):  
Carlos Breviglieri ◽  
Luis Gustavo L. Paula ◽  
William Wolf ◽  
Joao Luiz F. Azevedo
Keyword(s):  
High Order ◽  
Aerodynamic Flows ◽  
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.

Surface remeshing with robust high-order reconstruction

2014 ◽  
Vol 30 (4) ◽  
pp. 487-502 ◽  
Author(s):  
Navamita Ray ◽  
Tristan Delaney ◽  
Daniel R. Einstein ◽  
Xiangmin Jiao
Keyword(s):  
High Order ◽  
Order Reconstruction ◽  
Surface Remeshing ◽  
High Order Reconstruction

Assessment of Very High Order of Accuracy in Implicit LES models

2007 ◽  
Vol 129 (12) ◽  
pp. 1497-1503 ◽  
Author(s):  
Andrew Mosedale ◽  
Dimitris Drikakis
Keyword(s):  
Computational Cost ◽  
Single Mode ◽  
Theoretical Models ◽  
Higher Order ◽  
Second Order ◽  
High Order ◽  
Good Representation ◽  
Order Reconstruction ◽  
Time Required ◽  
Very High

This paper looks at the use of high-resolution and very high-order methods for implicit large-eddy simulation (ILES), with the specific example of simulating the multicomponent two-dimensional single-mode Richtmyer–Meshkov instability for which experimental data is available. The two gases are air and SF6, making stringent demands on the models used in the code. The interface between the two gases is initialized with a simple sinusoidal perturbation over a wavelength of 59mm, and a shock of strength Mach 1.3 is passed through this interface. The main comparison is between the second-order monotone upwind-centered scheme for conservation law methods of van Leer (1979, “Towards the Ultimate Conservative Difference Scheme,” J. Comput. Phys. 32, pp. 101–136) and the current state-of-the-art weighted essentially nonoscillatory interpolation, which is presented to ninth order, concentrating on the effect on resolution of the instability on coarse grids. The higher-order methods as expected provide better resolved and more physical features than the second-order methods on the same grid resolution. While it is not possible to make a definitive statement, the simulations have indicated that the extra time required for the higher-order reconstruction is less than the time saved by being able to obtain the same or better accuracy at lower computational cost (fewer grid points). It should also be noted that all simulations give a good representation of the growth rate of the instability, comparing very favorably to the experimental results, and as such far better than the currently existing theoretical models. This serves to further indicate that the ILES approach is capable of providing accurately physical information despite the lack of any formal subgrid model.

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