We focus here on a technique to compute compressible fluid flows in physical domains cluttered up with many small obstacles. This technique, referred to here as the integral formulation, consists in integrating the flow governing equations over the fluid part of control volumes including both fluid and solid zones; doing so, the integral of fluxes over solid boundaries may appear, for which expressions as a function of discrete variables must be provided. The integral formulation presents two essential advantages: first, we naturally recover the standard fluid approach when the mesh is refined; second, fluid/solid interactions may be, to some extent, modelled to recover the singular head losses at the interface between a free and a congested part of the computational domain. We apply here this approach to the Euler equations, using a collocated space discretization and a pressure correction algorithm, preserving the positivity of both the density and the internal energy. Verification test cases are performed, including a Riemann problem in a free domain and a shock wave reflection on a wall, using an equation of state which is suitable for weakly compressible fluid flows. Finally, we address a two-dimensional situation, where a shock wave impacts a set of obstacles; we observe a very encouraging agreement between the integral approach results and a CFD reference solution obtained with a pure fluid approach on a fine mesh.
We focus here on an integral approach to compute compressible inviscid fluid flows in physical domains cluttered up with many small obstacles. This approach is based on a multidimensional porous integral formulation of Euler system of equations. Its discretization uses a first order semi-implicit finite volume scheme with pressure-correction algorithm preserving the positivity of both density and pressure. Numerical tests are completed by simulating a 2D channel flow containing two aligned tubes. The results are compared to reference solutions obtained with a pure fluid approach on a fine mesh.
We discuss herein the suitability of some open boundary conditions. Considering the Euler system of gas dynamics, we compare approximate solutions of one-dimensional Riemann problems in a bounded sub-domain with the restriction in this sub-domain of the exact solution in the infinite domain. Assuming that no information is known from outside of the domain, some basic open boundary condition specifications are given, and a measure of the L 1-norm of the error inside the computational domain enables to show consistency errors in situations involving outgoing shock waves, depending on the chosen boundary condition formulation. This investigation has been performed with Finite Volume methods, using approximate Riemann solvers in order to compute numerical fluxes for inner interfaces and boundary interfaces.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.