Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Journal of Computational Physics
v-DSMV: a fast simulation method for rarefield flow
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Applied Numerical Analysis Using MATLAB
Applied Numerical Analysis Using MATLAB
Molecular Dynamics Simulation: Elementary Methods
Molecular Dynamics Simulation: Elementary Methods
A Galerkin Method for the Simulation of the Transient 2-D/2-D and 3-D/3-D Linear Boltzmann Equation
Journal of Scientific Computing
A Runge-Kutta discontinuous Galerkin method for viscous flow equations
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
A direct method for the Boltzmann equation based on a pseudo-spectral velocity space discretization
Journal of Computational Physics
Journal of Scientific Computing
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A high order numerical method for the solution of model kinetic equations is proposed. The new method employs discontinuous Galerkin (DG) discretizations in the spatial and velocity variables and Runge-Kutta discretizations in the temporal variable. The method is implemented for the one-dimensional Bhatnagar-Gross-Krook equation. Convergence of the numerical solution and accuracy of the evaluation of macroparameters are studied for different orders of velocity discretization. Synthetic model problems are proposed and implemented to test accuracy of discretizations in the free molecular regime. The method is applied to the solution of the normal shock wave problem and the one-dimensional heat transfer problem.