A Runge Kutta Discontinuous Galerkin approach to solve reactive flows on conforming hybrid grids: the parabolic and source operators

•Reactive Navier–Stokes equations solved by Runge–Kutta and Discontinuous Galerkin.•Parabolic and source terms are considered with no restrictive hypothesis.•Follow up of a previous paper studying the hyperbolic terms.•Parabolic terms use Van Leer’s Recovery and Borrel–Ryan’s Projection method.•This RKDG method is presented on structured, unstructured and hybrid grids.

A Runge–Kutta Discontinuous Galerkin method (RKDG) to solve the parabolic and source parts of reactive Navier–Stokes equations written in conservation form is presented. The parabolic operator uses a recent recovery method set up by van Leer for structured grids and a new projection method proposed by Borrel–Ryan for unstructured grids. The physical model involves complex chemistry and detailed transport. Transport coefficients are evaluated using algorithms which provide empirical expressions. In 1-D test cases the RKDG method is compared with a high order finite difference method. 2-D test cases in structured, unstructured and hybrid meshes are presented.