High-Order Non-Conservative Simulation of Hyperbolic Moment Models in Partially-Conservative Form

Finite-difference methods for simulation models incorporating non-conservative forces

We discuss algorithms applicable to the numerical solution of second-order ordinary differential equations by finite-differences. We make particular reference to the solution of the dissipative particle dynamics fluid model, and present extensive results comparing one of the algorithms discussed with the standard method of solution. These results show the successful modeling of phase separation...

Stable and conservative time propagators for second order hyperbolic systems

In this paper we construct a hierarchy of arbitrary high (even) order accurate explicit time propagators for semi-discrete second order hyperbolic systems. An accurate semi-discrete problem is obtained by approximating the corresponding spatial derivatives using high order accurate finite difference operators satisfying the summation by parts rule. In order to obtain a strictly stable semi-disc...

Accurate Numerical Discretizations of Non-conservative Hyperbolic Systems

We present an alternative framework for designing efficient numerical schemes for nonconservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics...

On the Riemann Problem for Non-conservative Hyperbolic Systems

A High Order Stable Conservative Method for Solving Hyperbolic Conservation Laws on Arbitrarily Distributed Point Clouds

In this paper, we aim to solve one and two dimensional hyperbolic conservation laws on arbitrarily distributed point clouds. The initial condition is given on such a point cloud, and the algorithm solves for point values of the solution at later time also on this point cloud. By using the Voronoi technique and by introducing a grouping algorithm, we divide the computational domain into non-over...