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DG Method
We consider the DG method to solve the hyperbolic conservation laws and study how to use the local projection limiting in the characteristic fields. Numerical experiments for 1D Riemann problem and 2D double Mach reflection problem are presented.
Hybrid compact-WENO Scheme
We investigate the performance of a hybrid compact-WENO finite difference scheme for numerical simulations of the detonation waves on uniformly discretized Cartesian domain.
RKDG Method
In the research, we mainly use the RKDG methods based on nonuniform mesh in 1D and unstructured mesh in 2D to solve Burgers equation as an example.
Hybrid WENO Scheme
Hybrid scheme is designed to solve multi-fluids Euler equation in its conservative form everywhere except at the material interfaces where the primitive form and the auxiliary advection equation are used instead.
Well-Balanced Nodal DG Method
Shallow water equation (SWE) is the hyperbolic systems of conservation laws with source terms (also called balance laws). To preserve exactly balance laws, here, we apply the well-balanced nodal DG meth-ods for 1D SWE as an example.
Fourier Conjugate Shock Detector
The solution of a hyperbolic conservation laws may have discontinuities, especially for problems containing both shocks and complicated smooth solution structures. The key idea is to detect such discontinuities using Fourier conjugate Method.