The Van Leer approach for the approximation of nonlinear scalar conservation laws is studied in one space dimension. The problem can be reduced to a nonlinear interpolation and we propose a convexity property for the interpolated values. We prove that under general hypotheses the method of lines in well posed in l ∩ BV and we give precise sufficient conditions to establish that the total variat...

We present a robust, highly accurate, and efficient positivity- boundedness-preserving diffuse interface method for the simulations of compressible gas-liquid two-phase flows with five-equation model by Allaire et al. using high-order finite difference weighted compact nonlinear scheme (WCNS) in explicit form. The equation states gas liquid are given ideal stiffened laws respectively. Under mil...

In this work, a steady discrete unified gas kinetic scheme (SDUGKS) is proposed to solve the radiative transfer equation (RTE), which an improvement of original SDUGKS [X. F. Zhou et al., J. Comput. Phys. 423, 109767 (2020)]. The trapezoidal rule other than rectangular used in adopted method reconstruction energy flux across cell interface, just as unsteady DUGKS. By way, length characteristic ...

Flux Vector Splitting (FVS) scheme is one group of approximate Riemann solvers for the compressible Euler equations. In this paper, the discretized entropy condition of the Kinetic Flux Vector Splitting (KFVS) scheme based on the gas-kinetic theory is proved. The proof of the entropy condition involves the entropy definition difference between the distinguishable and indistinguishable particles.