A parallel finite volume method for incompressible and slightly compressible reactive flows

Abstract

In this article, a parallel formulation of the finite volume method is presented for solving three-dimensional, turbulent, mixed, reactive, and slightly compressible flows. It can also be used for incompressible laminar/turbulent flows. The method is designed for nonorthogonal meshes, and oscillations caused by the advective terms are treated by a deferred correction technique. The chosen finite volume scheme is cell centered. The studied fluid is a single-phase multicomponent gas with Newtonian behavior. The focus is mainly on gas mixtures with predominance of N 2 $$ {}_2 $$ , since the chemical reaction of greatest interest is the combustion process in the air. The buoyancy is caused by the gradient of the specified mass, which is a function of the temperature and the composition of the gas mixture. The mathematical model uses an approximation for low Mach numbers, describing slightly compressible flows. The coupling between the fluid dynamic equations is given by the nonlinear Picard's method, with the pressure-velocity coupling treatment given by the SIMPLE algorithm (semi-implicit method for pressure-linked equations). The complete mathematical model includes the sensitive enthalpy equation for the conservation of energy. The LES (large eddy simulation) model is used for modeling the turbulence. The chemical reactions are implemented using the EDC (eddy dissipation concept) and the EDM (eddy dissipation model) approaches. The parallel strategy is based on a subdomain-by-subdomain approach, and uses the MPI and OpenMP standards in a hybrid parallel scheme. Compressed data structures are used to store the matrix coefficients.