Finite Volume Method for Level Set Equations on Polyhedral Meshes

Abstract: We propose a cell-centered finite volume method to numerically solve the G-equation model in premixed turbulent combustion. The G -equation is a standard level set equation containing the advective, normal, and mean curvature terms. Compared to conventional algorithms to solve level set equations on a polyhedron mesh, the proposed scheme has mainly three advantages. The first is that it numerically shows higher order of convergence on polyhedral meshes. The second is that the implementation of parallel computing using domain decomposition with 1-ring face neighborhood structure can be done straightforwardly by a standard cell-centered finite volume code. The third is that a time step restriction caused by the CFL condition is reduced by the proposed semi-implicit scheme. Numerical examples computed on polyhedral meshes are presented to verify the numerical properties of the proposed algorithm in the case of each velocity term in the G-equation.

Computer scienceMathematics

Audience: researchers in the topic

Modelling of materials - theory, model reduction and efficient numerical methods (UNCE MathMAC)