An implicit multigrid method for turbulent combustion

An implicit multigrid scheme for solving the Navier-Stokes, turbulence, spe cies, and variance transport equations describing turbulent combustion is p resented. Turbulence chemistry interaction is included by use of presumed p robability density functions (pdf). To avoid stiffness problems associated with chemically reacting flows, time integration is performed by an implici t LU-SGS algorithm. This requires the formation of a source term Jacobian. The complete, analytically derived Jacobian, including assumed pdf modeling , is given in the present paper. Thus, the high numerical stability of the original algorithm is maintained. Convergence acceleration is accomplished by a nonlinear multigrid method. Strongly nonlinear source terms in species , turbulence, and variance conservation equations usually keep multigrid me thods from converging. It is shown that freezing of coarse grid source term s including spatial derivatives and restriction damping in regions of high chemical activity may remedy this problem. Two finite-rate chemistry test c ases with methane and hydrogen combustion at supersonic speed demonstrate a strong reduction in required CPU time. (C) 2001 Academic Press.