An explicit algorithm that yields finite difference schemes of any desired order of accuracy for solving quasi-linear hyperbolic systems of partial differential equations in several space dimensions is presented. These schemes are shown to be stable under certain conditions. The stability conditions in the one-dimensional case are derived for any order of accuracy. Analytic stability proofs for...

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...

The nearly analytic discrete method (NADM) is a perturbation method originally proposed by Yang et al. (2003) [26] for acoustic and elastic waves in elastic media. This method is based on a truncated Taylor series expansion and interpolation approximations and it can suppress effectively numerical dispersions caused by the discretizating the wave equations when too-coarse grids are used. In the...

In this paper, we present a new fourth-order upwinding embedded boundary method (UEBM) over Cartesian grids, originally proposed in the Journal of Computational Physics (190, pp. 159, 2003) as a second-order method for treating material interfaces for Maxwell’s equations. In addition to the idea of the UEBM to evolve solutions at interfaces, we utilize the ghost fluid method to construct finite...

An optimal estimation method for state and distributed parameters in 1-D hyperbolic system based on adjoint method is proposed in this paper. A general form of the partial differential equations governing the dynamics of system is first introduced. In this equation, the initial condition or state variable as well as some empirical parameters are supposed to be unknown and need to be estimated. ...

The algebraic flux correction (AFC) schemes presented in this work constrain a standard continuous finite element discretization of nonlinear hyperbolic problem to satisfy relevant maximum principles and entropy stability conditions. desired properties are enforced by applying limiter antidiffusive fluxes that represent the difference between high-order baseline scheme property-preserving appro...

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...