Solution of the euler equations using the multigrid method

CONCLUSIONSA multigrid method for solving the incompressible Euler equations has been developed by exploiting factorizability of the governing differential operator. Treating each of the factors appropriately, optimal convergence rates have been attained. First order and second order discretization schemes are used for the momentum equations while a second order finite difference scheme is used for Poisson equation. No artificial viscosity is introduced in the discretization. Elements of the Full Approximation Scheme (FAS) multigrid algorithm, including relaxation, residuals, restriction, prolongation, cycle, and boundary treating have been presented in details. The algorithm is tested by solving a model problem (Euler equations on a rectangular domain) with known exact solution.