A semi-implicit scheme of inflow-based gradient (IBG) finite volume method is proposed to solve the G-equation model in premixed turbulent combustion. In order to overcome small time step caused by CFL restriction in polyhedron mesh, a semi-implicit method is used in IBG finite volume method inspired by (1, 2). Moreover, a conventional approximation of turbulent transport term in the G-variance equation is reviewed and compared with a mathematically correct tangential diffusion term. A sub-face tessellation technique is introduced to prevent deteriorating the order of convergence in case of distorted hexahedron cells. The implementation is very straightforward and easily combined with a conventional finite volume code. A higher order of convergence in numerical examples on polyhedron meshes is illustrated for each velocity term in the G-equation. Some numerical results in real engine cases are also presented.

(1) K. Mikula, M. Ohlberger, A New Level Set Method for Motion in Normal Direction Based on a Semi-Implicit Forward-Backward Diffusion Approach, SIAM Journal of Scientific Computing 32 (2010) 1527–1544.
(2) K. Mikula, M. Ohlberger, Inflow-Implicit/Outflow-Explicit Scheme for Solving Advection Equations, In: J.F. et al. (ed.) Finite Volumes for Complex Applications VI - Problems & Perspectives, Springer Proceedings in Mathematics 4 1 (2011) 683–691.