This paper is devoted to the construction of numerical fluxes for hyperbolic systems. We first present a GFORCE numerical flux, which is a weighted average of the Lax-Friedrichs and Lax-Wendroff fluxes. For the linear advection equation with constant coefficient, the new flux reduces identically to that of the Godunov first order upwind method. Then we incorporate GFORCE in the framework of the...

We develop a high order finite difference numerical boundary condition for solving hyperbolic conservation laws on a Cartesian mesh. The challenge results from the wide stencil of the interior high order scheme and the fact that the boundary intersects the grids in an arbitrary fashion. Our method is based on an inverse Lax-Wendroff procedure for the inflow boundary conditions. We repeatedly us...

In this paper, we implement energy equation coupled with viscous Burgers’ as a mathematical model for the estimation of thermal pollution river water. The is nonlinear system partial differential equations (PDEs) that read an initial and boundary value problem (IBVP). For numerical solution IBVP, investigate explicit second-order Lax- Wendroff type scheme parabolic PDEs. We present solutions gr...

Discrete updates of numerical partial differential equations (PDEs) rely on two branches temporal integration. The first branch is the widely-adopted, traditionally popular approach method-of-lines (MOL) formulation, in which multi-stage Runge-Kutta (RK) methods have shown great success solving ordinary (ODEs) at high-order accuracy. clear separation between and spatial discretizations governin...

ADER schemes are numerical methods, which can reach an arbitrary order of accuracy in both space and time. They are based on a reconstruction procedure and the solution of generalized Riemann problems. However, for general boundary conditions, in particular of Dirichlet type, a lack of accuracy might occur if a suitable treatment of boundaries conditions is not properly carried out. In this wor...

When using high-order schemes to solve hyperbolic conservation laws in bounded domains, it is necessary properly treat boundary conditions so that the overall accuracy and stability are maintained. In [1, 2] a finite difference treatment method proposed for Runge-Kutta methods of laws. The combines an inverse Lax-Wendroff procedure WENO type extrapolation achieve desired stability. this paper, ...

Abstract We study the following wave equation $$u_{tt}-\Delta u+\alpha (t)\left| u_{t}\right| ^{m(\cdot )-2}u_{t}=0$$ u tt - Δ + α ( t ) <mm...

We present a solver of 3D two-fluid plasma model for the simulation short-pulse laser interactions with plasma. This resolves equations ideal gas closure. also include Bhatnagar-Gross-Krook collision model. Our is based on PseudoSpectral Time-Domain (PSTD) method to solve Maxwell's curl equations. use Strang splitting integrate Euler source term: while are solved composite scheme mixing Lax-Fri...