An investigation on the explicit large-time step scheme in the density-based two-phase flow solver
The two-phase flow six-equation model is a hyperbolic non-conservative system,with non-equilibrium source terms.The density-based numerical method contains the solution of the homogeneous hyperbolic equations and relaxation of the non-equilibrium source terms.In the solution of homogeneous equations,the time step with Godunov's scheme is limited by the CFL number less than 1,which leads to low computation efficiency.The large time step scheme is one of the important methods to break the limit in hyperbolic conservative equations.Under the linear wave assumption,this research extends the flux-difference splitting type of LTS scheme to solving the non-conservative two-phase six-equation model and proposes the LTS scheme(LTS-HLLC)based on HLLC type Riemann solver.It is found that increasing the CFL number with the LTS-HLLC scheme can reduce the numerical viscosity in two-phase regions with obvious interfaces,improve the resolution of the discontinuity,like shocks,and produce oscillations easily,which is the same as those in the hyperbolic conservative equations with the LTS scheme.However,in two-phase mixture regions,increasing CFL number can enhance the diffusion of the relaxation process,reducing the resolution of the discontinuity.Increasing the CFL number with LTS-HLLC scheme can effectively reduce the CPU time and improve the computation efficiency.
two-phase flowlarge time stepnon-conservative equationsrelaxation methodwave adding method
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