A sixth-order accurate staggered finite volume scheme for the incompressible Navier-Stokes and Euler equations on unstructured meshes

We propose a sixth-order staggered finite volume scheme based on polynomial reconstructions to achieve high accurate numerical solutions for the incompressible NavierStokes and Euler equations. The scheme is equipped with a fixed-point algorithm with solution relaxation to speed-up the convergence and reduce the computation time. Numerical tests are provided to assess the effectiveness of the method to achieve up to sixth-order conR. Costa Institut de Mathématiques de Toulouse, Université Paul Sabatier, 31062 Toulouse, France and Centro de Matemática, Universidade do Minho, Campus de Azurém, 4800-058 Guimarães, Portugal Tel.: +351-253-510400 Fax: +351-253-510401 E-mail: [email protected] S. Clain Centro de Matemática, Universidade do Minho, Campus de Azurém, 4800-058 Guimarães, Portugal and Institut de Mathématiques de Toulouse, Université Paul Sabatier, 31062 Toulouse, France Tel.: +351-253-510400 Fax: +351-253-510401 E-mail: [email protected] G.J. Machado Centro de Matemática, Universidade do Minho, Campus de Azurém, 4800-058 Guimarães, Portugal Tel.: +351-253-510400 Fax: +351-253-510401 E-mail: [email protected] R. Loubère Institut de Mathématiques de Toulouse, Université Paul Sabatier, 31062 Toulouse, France Tel.: +33-561557652 Fax: +33-561558385 E-mail: [email protected] 2 Ricardo Costa et al. vergence rates. Simulations for the benchmark lid-driven cavity problem are also provided to highlight the benefit of the proposed high-order scheme.