Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy
This paper concerns a finite difference scheme for numerical integration of the hyperbolic conservation law problems \[ U_t+\text{div } F(U)=0, \] where \(U\in {\mathbb R^m}\), \(F(U)\in {\mathbb R^d}\), and \(F\) represents the flux. The right-hand-side of this equation is transformed by introduction of the numerical flux on the space grid, and the problem is treated as a system of ordinary differential equations. To integrate this system numerically a special kind of explicite Runge-Kutta method is used. In order to insure the possibly high order of accuracy a special technique of interpolation with delimiters is used. This technique allows also to estimate (locally) the regularity of the solution and to preserve the monotonicity. The paper contains tables of coefficients of interpolation formulas. The results of numerical tests are presented.
weighted essentially nonoscillatory schemes
scientific article; zbMATH DE number 1462879
scientific article