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...

A new two-distribution lattice Boltzmann equation (LBE) algorithm is presented to solve the laminar diffusion flames within the context of Burke–Schumann flame sheet model. One distribution models the transport of the Schvab–Zeldovich coupling function, or the mixture fraction to combine the energy and species equations. The other distribution models the quasi-incompressible Navier–Stokes equat...

This exploratory work tries to present first results of a novel approach for the numerical approximation of solutions of hyperbolic systems of conservation laws. The objective is to define stable and “reasonably” accurate numerical schemes while being free from any upwind process and from any computation of derivatives or mean Jacobian matrices. That means that we only want to perform flux eval...

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...

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 ...

A general methodology is introduced to build conservative numerical models for fluid simulations based on segregated schemes, where mass, momentum, and energy equations are solved by different methods. It especially designed here developing new discretizations of the total equation adapted a thermal coupling with lattice Boltzmann method (LBM). The proposed linear equivalence standard entropy e...

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 discontinuous Galerkin (DG) or local discontinuous Galerkin (LDG) method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters. The LaxWendroff time discretization procedure is an alternative method for time d...

In this paper, we propose a high order residual distribution conservative finite difference scheme for solving steady state hyperbolic conservation laws on non-smooth Cartesian or other structured curvilinear meshes. WENO (weighted essentially non-oscillatory) integration is used to compute the numerical fluxes based on the point values of the solution, and the principles of residual distributi...