非定常移流方程式に対する高次精度TVD時間進行法の比較・検討

概要

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Time marching methods coupled with a third order upwind TVD scheme are compared from the viewpoints of accuracy, memory requirement and computational cost. The methods examined are the second and the third order Runge-Kutta presented by Shu and Osher, the explicit Euler, the second order Adams-Bashforth, the implicit Euler and the Crank-Nicolson methods. Benchmark problems on time-dependent linear advective transport are solved using these methods. As a result, the Shu and Osher's Runge-Kutta methods of the second and the third order are recommended. The explicit Euler method suffers from oversteepening of the gradient due to numerical diffusion with a negative coefficient. The Adams-Bashforth method is inferior to the Runge-Kutta method in accuracy and memory requirement. The Crank-Nicolson method produces solutions as accurate as the Runge-Kutta method, but requires much CPU time due to the nonlinear feature of the TVD flux limiter.
一般社団法人日本機械学会の論文
1995-06-25