Synthesis of the Results with the Finite-Volume Method

Six contributions to the workshop used the finite-volume method to discretize the spatial derivatives in order to numerically solve the benchmark problem. The domain is covered with a staggered grid, in which finite-volumes are defined. The equations are solved using the primitive-variables formulation. The transport equations for mass, momentum and energy are integrated over each finite volume. The convection and diffusion fluxes through the boundaries of the volumes are discretized by finite differences. Also the time derivatives are discretized by finite differences. The accuracy depends on the order of the accuracy of the finite-difference discretization of the fluxes and time derivatives, and on the number of spatial grid points and the magnitude of the time step. The transport variables (in the case of an implicit time integration scheme) and the pressure are only implicitly known at each next time level; a solver has to be selected to explicitly calculate the unknowns. Both the accuracy and the choice for the solver determine the magnitude of the computational effort.