On the construction of high order finite volume methods

Abstract

This paper presents a family of high order finite volume schemes applicable on general shaped control volumes. These schemes are based on the k-exact reconstruction and a procedure similar to the WENO reconstruction is introduced through the secondary reconstructions. A new limiter based on the weighted biased averaging procedure is proposed to ensure efficient and robust shock capturing capabilities of the finite volume schemes. Several test cases are presented to study the performance of the proposed schemes. They show that the numerical schemes of the present paper can predict the smooth fields with uniformly high order accuracy and can capture the shock waves and contact discontinuities in high resolution. © 2011 Springer-Verlag Berlin Heidelberg.