• Publications
  • Influence
Hyperbolic divergence cleaning for the MHD equations
In simulations of magnetohydrodynamic (MHD) processes the violation of the divergence constraint causes severe stability problems. In this paper we develop and test a new approach to theExpand
Numerical Schemes for Conservation Laws
Initial Value Problems for Scalar Conservation Laws in 1-D. Initial Value Problems for Scalar Conservation Laws in 2-D. Initial Value Problems for Systems in 1-D. Initial Value Problems for SystemsExpand
A posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multi dimensions
TLDR
In this paper we derive a posteriori error estimates in the L 1 -norm for upwind finite volume schemes for the discretization of nonlinear conservation laws on unstructured grids in multi dimensions. Expand
Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system
We present the convergence analysis of locally divergence-free discontinuous Galerkin methods for the induction equations which appear in the ideal magnetohydrodynamic system. When we use a secondExpand
Measure-valued Solutions of the Euler Equations for Ideal Compressible Polytropic Fluids
The existence of global measure-valued solutions to the Euler equations describing the motion of an ideal compressible and heat conducting fluid is proved. The motion is considered in a boundedExpand
Convergence of upwind finite volume schemes for scalar conservation laws in two dimensions
This paper proves the convergence of a general class of monotone finite volume methods for numerical schemes of scalar conservation laws in two dimensions on unstructured meshes. There areExpand
Numerical Solutions to Compressible Flows in a Nozzle with Variable Cross-section
TLDR
Compressible flows in a nozzle can be modeled by the gas dynamics equations in one-dimensional space with stationary waves . Expand
The Sharp-Interface Limit for the Navier–Stokes–Korteweg Equations
We investigate the sharp-interface limit for the Navier–Stokes–Korteweg model, which is an extension of the compressible Navier–Stokes equations. By means of compactness arguments, we show thatExpand
Convergence of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions
Summary. We prove convergence of a class of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions. The result is applied to theExpand
A robust numerical method for approximating solutions of a model of two-phase flows and its properties
TLDR
The objective of the present paper is to extend our earlier works on simpler systems of balance laws in nonconservative form such as the model of fluid flows in a nozzle with variable cross-section to a more complicated system consisting of seven equations which has applications in modeling of deflagration-to-detonation transition in granular materials. Expand
...
1
2
3
4
5
...