Why nonconservative schemes converge to wrong solutions: error analysis

Localization effects and measure source terms in numerical schemes for balance laws

Mathematics of Computation

Discrete equations for physical and numerical compressible multiphase mixtures

Journal of Computational Physics

Stable and accurate hybrid finite volume methods based on pure convexity arguments for hyperbolic systems of conservation law

Journal of Computational Physics

Variable-order finite elements and positivity preservation for hyperbolic PDEs

Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs

A thermodynamically consistent and fully conservative treatment of contact discontinuities for compressible multicomponent flows

Journal of Computational Physics

Preserving positivity for hyperboilic PDEs using variable-order finite elements with bounded polynomials

Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation

Asymptotic preserving and positive schemes for radiation hydrodynamics

Journal of Computational Physics

Why many theories of shock waves are necessary: Kinetic functions, equivalent equations, and fourth-order models

Journal of Computational Physics

Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes

Journal of Computational Physics

Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures

Journal of Computational Physics

FORCE schemes on unstructured meshes I: Conservative hyperbolic systems

Journal of Computational Physics

High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems

Journal of Scientific Computing

An all-speed relaxation scheme for interface flows with surface tension

Journal of Computational Physics

Finite volume multischeme for hyperbolic conservation laws

FANDB'09 Proceedings of the 2nd WSEAS international conference on Finite differences, finite elements, finite volumes, boundary elements

Preserving positivity for hyperbolic PDEs using variable-order finite elements with bounded polynomials

Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation

Convergence of Linearized and Adjoint Approximations for Discontinuous Solutions of Conservation Laws. Part 1: Linearized Approximations and Linearized Output Functionals

SIAM Journal on Numerical Analysis

On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System

Journal of Scientific Computing

A Conservative Method for the Simulation of the Isothermal Euler System with the van-der-Waals Equation of State

Journal of Scientific Computing

On the Convergence and Well-Balanced Property of Path-Conservative Numerical Schemes for Systems of Balance Laws

Journal of Scientific Computing

A Simple Extension of the Osher Riemann Solver to Non-conservative Hyperbolic Systems

Journal of Scientific Computing

WENO Scheme with Subcell Resolution for Computing Nonconservative Euler Equations with Applications to One-Dimensional Compressible Two-Medium Flows

Journal of Scientific Computing

Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: Theory and boundary conditions

Journal of Computational Physics

Direct numerical simulation of interfacial instabilities: A consistent, conservative, all-speed, sharp-interface method

Journal of Computational Physics

Output-based mesh adaptation for high order Navier-Stokes simulations on deformable domains

Journal of Computational Physics

Accurate numerical modeling of 1D flow in channels with arbitrary shape. Application of the energy balanced property

Journal of Computational Physics