A robust shock-capturing scheme based on rotated Riemann solvers

SUMMARYIn this paper, a new high-order and high-resolution method called the Runge-Kutta control volume discontinuous finite element method (RKCVDFEM) was proposed to solve 1D and 2D systems of hyperbolic conservation laws. Its main advantage lies in the local conservation, and it is simpler than the RungeKutta discontinuous Galerkin finite element method (RKDGM). The theoretical analysis showed that the RKCVDFEM has formally an optimal convergence order for 1D systems. Based on logically rectangular grids of irregular quadrilaterals, a scheme for 2D systems was constructed. Some classical problems were simulated and the validity of the method was presented.

“…Compared with [13][14][15][16][17][18][19][20], the results given by the RKCVDFEM are satisfied. For all tests, we take M = 50, cfl = …”

Section: Numerical Resultsmentioning

confidence: 94%

“…We use TVB second-order Runge-Kutta method introduced in Section 2.1.2 to solve ODEs (20) and define cfl number as follows: …”

Section: Temporal Discretization and Limitermentioning

confidence: 99%

The Runge–Kutta control volume discontinuous finite element method for systems of hyperbolic conservation laws

Chen

2010

“…However, the main disadvantage of this method is its inefficiency in computation and the CPU time is about twice than that in the original HLLC solver. In [18], the CPU time ratio is about 1.5 for rotated Roe solver and the case will not happen in rotated HLLC solver. It is because the former is a linear solver and the latter belongs to nonlinear solver.…”

Section: Rotated Methods For Hllc Solvermentioning

confidence: 99%

“…In order to respect the multidimensional nature of the Euler equations and reduce the grid-dependence of conventional schemes, Levy et al [17] gave a rotated Riemann solver that used flow parameters to determine the direction. Ren [18] put forward a rotated Roe Riemann solver to eliminate the shock instability, where the upwind direction is determined by the velocity-difference vector. The rotated method is based on the decomposition of n, which is the outward unit vector normal to face, into two orthogonal directions.…”

Section: Rotated Methods For Hllc Solvermentioning

confidence: 99%

See 1 more Smart Citation

Cures for numerical shock instability in HLLC solver

Huang

Wei

et al. 2011

SUMMARYIn this paper, we proposed two methods to cure the numerical shock instability for HLLC Riemann solver in two-dimension finite volume Euler codes. One method (Ren Yu-Xin, Computers and Fluids 2003; 32:1379-1403) uses the rotated method and another one (Hao Wu et al., submitted) is the hybrid method. Taking into account the efficiency, accuracy and robustness, the hybrid method is better than rotated method for HLLC solver. A series of test problems prove this conclusion.

Developing a hybrid flux function suitable for hypersonic flow simulation with high‐order methods

Wang

Deng

Wang

et al. 2015

SUMMARYIn this paper, we develop a new hybrid Euler flux function based on Roe's flux difference scheme, which is free from shock instability and still preserves the accuracy and efficiency of Roe's flux scheme. For computational cost, only 5% extra CPU time is required compared with Roe's FDS. In hypersonic flow simulation with high-order methods, the hybrid flux function would automatically switch to the Rusanov flux function near shock waves to improve the robustness, and in smooth regions, Roe's FDS would be recovered so that the advantages of high-order methods can be maintained. Multidimensional dissipation is introduced to eliminate the adverse effects caused by flux function switching and further enhance the robustness of shock-capturing, especially when the shock waves are not aligned with grids. A series of tests shows that this new hybrid flux function with a high-order weighted compact nonlinear scheme is not only robust for shock-capturing but also accurate for hypersonic heat transfer prediction.