We introduce a new family of Godunov-type semi-discrete central schemes for multidimensional Hamilton–Jacobi equations. These schemes are a less dissipative generalization of the central-upwind schemes that have been recently proposed in Kurganov, Noelle and Petrova (2001, SIAM J. Sci. Comput., 23, pp. 707–740). We provide the details of the new family of methods in one, two, and three space di...

We develop new central-upwind schemes for nonlinear elasticity equations in a heterogeneous medium. Finite volume central-upwind schemes consist of three steps: reconstruction, evolution, and projection onto the original grid. In our new method, the evolution is performed in the standard way by integrating the system over the space-time control volumes. However, the reconstruction and projectio...

We discover that the choice of a piecewise polynomial reconstruction is crucial in computing solutions of nonconvex hyperbolic (systems of) conservation laws. Using semi-discrete central-upwind schemes we illustrate that the obtained numerical approximations may fail to converge to the unique entropy solution or the convergence may be so slow that achieving a proper resolution would require the...

This paper concerns numerical methods for two-phase flows. The governing equations are the compressible 2-velocity, 2-pressure flow model. Pressure and velocity relaxation are included as source terms. Results obtained by a Godunov-type central scheme and a Roe-type upwind scheme are presented. Issues of preservation of pressure equilibrium, and positivity of the partial densities are addressed...

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side whi...

The two-phase drift flux model is extensively used in multiphase flow applications. In this study, we focus on possible numerical schemes for solving the model. Due to complexity of primitive equations and empirical parameters, it challenging achieve stability scheme high resolution second order central scheme, central-upwind third fifth weighted essentially non-oscillatory (WENO) were successf...

The results of computations with eight explicit finite difference schemes on a suite of one-dimensional and two-dimensional test problems for the Euler equations are presented in various formats. Both dimensionally split and two-dimensional schemes are represented, as are central and upwind-biased methods, and all are at least second-order accurate.