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Two-Dimensional Riemann Problem for Burgers' Equation
윤대기,황운재 대한수학회 2008 대한수학회보 Vol.45 No.1
In this paper, we construct the analytic solutions and nu-merical solutions for a two-dimensional Riemann problem for Burgers’equation. In order to construct the analytic solution, we use the charac-teristic analysis with the shock and rarefaction base points. We apply thecomposite scheme suggested by Liska and Wendro to compute numer-ical solutions. The result is coincident with our analytic solution. Thisdemonstrates that the composite scheme works pretty well for Burgers’equation despite of its simplicity.
Adaptive mesh refinement for weighted essentially non-oscillatory schemes
윤대기,Hongjoong Kim,황운재 대한수학회 2008 대한수학회보 Vol.45 No.4
In this paper, we describe the application procedure of the adaptive mesh refinement (AMR) for the weighted essentially non-oscillatory schemes (WENO), and observe the effects of the derived algorithm when problems have piecewise smooth solutions containing discontinuities. We find numerically that the dissipation of the WENO scheme can be lessened by the implementation of AMR while the accuracy is maintained. We deduce from the experiments that the AMR-implemented WENO scheme captures shocks more efficiently than the WENO method using uniform grids. In this paper, we describe the application procedure of the adaptive mesh refinement (AMR) for the weighted essentially non-oscillatory schemes (WENO), and observe the effects of the derived algorithm when problems have piecewise smooth solutions containing discontinuities. We find numerically that the dissipation of the WENO scheme can be lessened by the implementation of AMR while the accuracy is maintained. We deduce from the experiments that the AMR-implemented WENO scheme captures shocks more efficiently than the WENO method using uniform grids.