High-order residual-based compact schemes for compressible inviscid flows

A residual-based compact scheme, previously developed to compute d-dimensional inviscid compressible flows with third-order accuracy on a 3d-point stencil [Lerat A, Corre C. Residual-based compact schemes for multidimensional hyperbolic system of conservation laws. Comput Fluids 2002;31:639–61], is generalized to larger stencils allowing to reach a very high order of accuracy. Compactness is retained since for instance a seventh-order accurate dissipative approximation can be achieved on a 5d-point stencil, without requiring the linear system solutions associated with usual compact schemes. The high-order generalization is also performed for unsteady flows. Applications to model problems and unsteady inviscid flows are presented.