High-order CESE schemes

Abstract

This chapter is dedicated to the description of high-order CESE schemes. In the second-order CESE schemes, the first-order Taylor expansion was employed to approximate the unknowns and fluxes within the solution elements. The accuracy of the scheme mainly depends on the approximations on the surfaces of the conservation elements. Analogously, the high-order CESE schemes with Mth-order in space and time are generally derived from (M−1)th-order Taylor expansions in the solution elements. The high-order CESE schemes use a highly compact stencil. Furthermore, spatial and temporal high-order accuracy can be achieved simultaneously. We shall start with constructing a 1D high-order scheme and then extend it to multi-dimensional schemes.