Slope limitation in the higher-order FVM for hyperbolic problems

Abstract

The new limitation procedure is proposed in the polynomial reconstruction of the piecewise constant data. It is based on the discontinuity indicator used in the discontinuous finite element method.

The limitation procedure is applied in the framework of the higher-order ADER type Finite Volume Method (FVM). The proposed strategy and the efficiency of the method is demonstrated on the physically relevant numerical example.

Keywords

• Euler equations
• shallow water equations
• finite volume method
• higher-order method
• polynomial reconstruction
• slope limiter