A two-dimensional fourth-order unstructured-meshed Euler solver based on the CESE method

Tetrahedral-Mesh Simulation of Turbulent Flows with the Space-Time Conservative Schemes

“…High-order accuracy has also been established for the linear advection equation, linearized and non-linear Euler equations. 7,[19][20] In this article, interactions of waves, vortex, or isotropic turbulence with normal or bow shocks are studied using unstructured triangular or tetrahedral meshes to assess the performance of the space-time conservative CESE schemes. In addition, numerical computations are also performed for three-dimensional decaying isotropic turbulence (with a high turbulent Mach number) and the inviscid Taylor-Green vortex.…”

A class of high-order weighted compact central schemes for solving hyperbolic conservation laws

“…There are plenty of other variations of WENO schemes which we are not going to review here. One major strategy to build compact high-order schemes is increasing the internal DOF, such as the discontinuous Galerkin (DG) scheme [35,36,37,38,39], the compact least-squares finite-volume (CLSFV) scheme [40,41,42], the high-order CESE scheme [43,44,45], the spectral volume (SV) scheme [46,47,48], the spectral difference (SD) scheme [49,50]. The DG, CLSFV and CESE schemes increase the internal DOF by increasing the degree of the polynomial, while SV and SD schemes increase the internal DOF by increasing the number of sub-cells and sub-points respectively.…”

“…This approach repeatedly uses the original partial differential equations (PDEs) to calculate all the space-time information so that the scheme can achieve high-order accuracy within only one time-step. Because of the one-time-step feature, the Lax-Wendroff-type time discretization has been used in many schemes, such as the original ENO scheme [23], the WENO finite difference scheme with Lax-Wendroff-type time discretization [56], the DG scheme with Lax-Wendroff-type time discretization [57], the P N P M scheme [51,52,53], the ADER (arbitrary high-order schemes utilizing high-order derivatives) scheme [58,59,60,61], the CESE scheme [19,20,45,43,44], and so forth.…”