An analysis of finite-difference and finite-volume formulations of conservation laws
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Solving the MHD equations by the space-time conservation element and solution element method
Journal of Computational Physics
Application of space-time CE/SE method to shallow water magnetohydrodynamic equations
Journal of Computational and Applied Mathematics
Mathematics and Computers in Simulation
On the application of a variant CE/SE method for solving two-dimensional ideal MHD equations
Applied Numerical Mathematics
The space-time CESE method for solving special relativistic hydrodynamic equations
Journal of Computational Physics
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In this paper, we report a version of the space-time conservation element and solution element (CE/SE) method in which the 2D and 3D unsteady Euler equations are simulated using structured or unstructured quadrilateral and hexahedral meshes, respectively. In the present method, mesh values of flow variables and their spatial derivatives are treated as independent unknowns to be solved for. At each mesh point, the value of a flow variable is obtained by imposing a flux conservation condition. On the other hand, the spatial derivatives are evaluated using a finite-difference/weighted-average procedure. Note that the present extension retains many key advantages of the original CE/SE method which uses triangular and tetrahedral meshes, respectively, for its 2D and 3D applications. These advantages include efficient parallel computing, ease of implementing nonreflecting boundary conditions, high-fidelity resolution of shocks and waves, and a genuinely multidimensional formulation without the need to use a dimensional-splitting approach. In particular, because Riemann solvers-- the cornerstones of the Godunov-type upwind schemes--are not needed to capture shocks, the computational logic of the present method is considerably simpler. To demonstrate the capability of the present method, numerical results are presented for several benchmark problems including oblique shock reflection, supersonic flow over a wedge, and a 3D detonation flow.