Published in International Journal for Numerical Methods in Fluids Vol. 70' (1), pp. 1-19, 2012
DOI: 10.1002/fld.2674

Abstract

In this paper, we propose a computational algorithm for the solution of thermally coupled flows in subsonic regime. The formulation is based upon the compressible Navier–Stokes equations, written in nonconservation form. An efficient modular implementation is obtained by solving the energy equation separately and then using the computed temperature as a known value in the momentum‐continuity system. If an explicit single‐step time integration scheme for the energy equation is used, the decoupling results to be natural.

Integration of the momentum‐continuity system is carried out using a semi‐explicit method, combining Runge–Kutta and Backward Euler schemes for the momentum and continuity equations, respectively. Implicit treatment of pressure leads to favorable time step estimates even in the low Mach number (Ma ≪ 1) regimes. The numerical dissipation introduced by the Backward Euler scheme ensures absence of the spurious high frequencies in the numerical solution.

The key point of the method is the assumption of linear variation of the temperature within a time step. Combined with a fractional splitting of the momentum‐continuity system, it allows to solve the continuity only once per time step. Omitting the necessity of solving for the pressure at every intermediate step of the Runge–Kutta scheme minimizes the computational cost associated to the implicit step and leads to an efficiency close to that of a purely explicit scheme.

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