Residual-based compact schemes for multidimensional hyperbolic systems of conservation laws

Abstract

Dissipative compact schemes are constructed for multidimensional hyperbolic problems. High-order accuracy is not obtained for each space derivative, but for the whole residual, which avoids any linear algebra. Numerical dissipation is also residual based, i.e. constructed from derivatives of the residual only, which provides simplicity and robustness. High accuracy and efficiency are checked on 2-D and 3-D model problems. Various applications to the compressible Euler equations without and with shock waves are presented.