We have recently introduced a new cell-centered Lax-Wendroff HLL hybrid scheme for Lagrangian hydrodynamics [Fridrich et al. J. Comp. Phys. 326 (2016) 878-892] with results presented only on logical rectangular quadrilateral meshes. In this study we present an improved version unstructured meshes, including uniform triangular and hexagonal meshes non-uniform polygonal The performance of the is ...

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. ...

In this paper, we study the stability of a numerical boundary treatment high order compact finite difference methods for parabolic equations. The schemes could achieve very accuracy with relatively small stencils. To match convergence in interior domain, take simplified inverse Lax–Wendroff (SILW) procedure (Tan et al., 2012; Li 2017) as our treatment. third total variation diminishing (TVD) Ru...

This note presents a preliminary study of the supra-convergence of well-balanced (finite volume) schemes for conservation laws with a (nonlinear) geometrical source term. In particular, we consider scalar (linear) advection equations in one dimension, for which smooth analytical solutions are available, and upwind interfacial discretizations for the numerical simulation on nonuniform grids (als...

2.1 Examples of conservative schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.1 The Godunov Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.2 The Lax-Friedrichs Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 The local Lax-Friedrichs Scheme . . . . . . . ....

One cycle of a composite finite difference scheme is defined as several time steps of an oscillatory scheme such as Lax–Wendroff followed by one step of a diffusive scheme such as Lax–Friedrichs. We apply this idea to gas dynamics in Lagrangian coordinates. We show numerical results in two dimensions for Noh’s infinite strength shock problem and the Sedov blast wave problem, and for several one...

Abstract Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical to solve steady-state solutions hyperbolic partial differential equations (PDEs). The Gauss-Seidel iterations and alternating strategy used cover characteristics PDEs in each order achieve convergence rate solutions. A nice property fixed-point which distinguishes them from other is that they explicit ...

Abstract A number of physical processes in laser-plasma interaction can be described with the two-fluid plasma model. We report on a solver for three-dimensional model equations. This is particularly suited simulating between short laser pulses plasmas. The fluid relies two-step Lax–Wendroff split fourth-order Runge–Kutta scheme, and we use Pseudo-Spectral Analytical Time-Domain (PSATD) method ...

ABSTRACT The conservative high-order accurate spectral difference method is presented for simulation of rotating shallowwater equations. The method is formulated using Lagrange interpolations on Gauss-Lobatto points for the desired order of accuracy without suffering numerical dissipation and dispersion errors. The optimal third-order total variation diminishing (TVD) Runge-Kutta algorithm is u...