Related papers: Numerical schemes for coupled systems of nonconser…
The author presented a stochastic and variational approach to the Lax-Friedrichs finite difference scheme applied to hyperbolic scalar conservation laws and the corresponding Hamilton-Jacobi equations with convex and superlinear…
We have undertaken an algorithmic search for new integrable semi-discretizations of physically relevant nonlinear partial differential equations. The search is performed by using a compatibility condition for the discrete Lax operators and…
This paper considers the optimal control for hybrid systems whose trajectories transition between distinct subsystems when state-dependent constraints are satisfied. Though this class of systems is useful while modeling a variety of…
This paper deals with the numerical (finite volume) approximation of reaction-diffusion systems with relaxation, among which the hyperbolic extension of the Allen--Cahn equation represents a notable prototype. Appropriate discretizations…
In this paper, we propose an adaptive high-order method for hyperbolic systems of conservation laws. The proposed method is based on a dual formulation approach: Two numerical solutions, corresponding to conservative and nonconservative…
In this paper, we investigate numerically a diffuse interface model for the Navier-Stokes equation with fluid-fluid interface when the fluids have different densities \cite{Lowengrub1998}. Under minor reformulation of the system, we show…
For nonlinear hyperbolic systems of conservation laws in one space variable, we establish the existence of nonclassical entropy solutions exhibiting nonlinear interactions between shock waves with strong strength. The proposed theory is…
The relation between Latttice Boltzmann Method, which has recently become popular, and the Kinetic Schemes, which are routinely used in Computational Fluid Dynamics, is explored. A new discrete velocity model for the numerical solution of…
We consider coupled models for particulate flows, where the disperse phase is made of particles with distinct sizes. We are thus led to a system coupling the incompressible Navier-Stokes equations to the multi-component Vlasov-Fokker-Planck…
A novel Lattice Boltzmann Method applicable to compressible fluid flows is developed. This method is based on replacing the governing equations by a relaxation system and the interpretation of the diagonal form of the relaxation system as a…
A semi-implicit Lax-Wendroff scheme is developed for electron-phonon coupling process in metals based on the two-temperature kinetic equations. The core of this method is to integrate the evolution information of physical equations into the…
We investigate a high-order, fully explicit, asymptotic-preserving scheme for a kinetic equation with linear relaxation, both in the hydrodynamic and diffusive scalings in which a hyperbolic, resp. parabolic, limiting equation exists. The…
The Osher-Chakrabarthy family of linear flux-modification schemes is considered. Improved lower bounds on the compression factors are provided, which suggest the viability of using the unlimited version. The LLF flux formula is combined…
A novel numerical scheme including time and spatial discretization is offered for coupled Cahn-Hilliard and Navier-Stokes governing equation sys-tem in this paper. Variable densities and viscosities are considered in the nu-merical scheme.…
We extend the convergence analysis for methods solving PDE-constrained optimal control problems containing both discrete and continuous control decisions based on relaxation and rounding strategies to the class of first order semilinear…
We are interested in a class of numerical schemes for the optimization of nonlinear hyperbolic partial differential equations. We present continuous and discretized relaxation schemes for scalar, one-- conservation laws. We present…
In this paper, we study a hyperbolic relaxation of the viscous Cahn--Hilliard system with zero Neumann boundary conditions. In fact, we consider a relaxation term involving the second time derivative of the chemical potential in the first…
We study numerically the standard one pressure model of two fluid flows with energy equations. This system is not solved in time derivative. It has been transformed into an equivalent system solved in time derivative. We show that the…
In this paper, we introduce a framework for the discretization of a class of constrained Hamilton-Jacobi equations, a system coupling a Hamilton-Jacobi equation with a Lagrange multiplier determined by the constraint. The equation is…
Numerical schemes for the general relativistic hydrodynamic equations are discussed. The use of conservative algorithms based upon the characteristic structure of those equations, developed during the last decade building on ideas first…