A compact residual-based scheme for solving the compressible Euler and Navier-Stokes equations

摘要

A dissipative compact scheme is presented for solving the steady compressible Euler and Navier-Stokes equations with a third-order accuracy. High-order accuracy is not obtained for each space derivative but for the whole residual, which avoids any linear algebra and provides compactness. Numerical dissipation is also constructed from derivatives of the residual only, providing simplicity and robustness. Applications of the scheme to model test-cases as well as compressible flows are presented.