The Artificial Compressibility Method (ACM) for the incompressible NavierStokes equations is (link-wise) reformulated (referred to as LW-ACM) by a finite set of discrete directions (links) on a regular Cartesian mesh, in analogy with the Lattice Boltzmann Method (LBM). The main advantage is the possibility of exploiting well established technologies originally developed for LBM and classical co...

Lattice Boltzmann method is relatively new method in the field of computational fluid dynamics. It has been derived from lattice gas automata and is still under development. Basic steps of the LBM (collision, streaming, boundary conditions, macroscopic quantities) will be presented. Comparison with the finite difference method that uses Navier-Stokes equation on a lid driven cavity benchmark te...

A numerical analysis of non-Darcian flow to a pumping well in a confined aquifer using the strong-form mesh-free (MFREE) method is described. This technique is targeted at problems that use advanced numerical approaches for modeling non-Darcian flow and it supports the assumption that the non-Darcian flow follows the Forchheimer equation. Interpolation functions including the multi-quadrics (MQ...

This study modifies and discusses the application of a complete meshless method based on Shepard approximation with an emphasis on the detailed description of this computational technique and its numerical implementations. A new weighting function would be suggested. The global shape function and its derivatives are built based only on the discretisation of the domain in nodes. To deal with the...

SUMMARY Numerical Stability of the Finite Element/Finite Difference Time Domain Hybrid algorithm is dependent on the hybridization mechanism adopted. A framework is developed to analyze the numerical stability of the hybrid time marching algorithm. First, the global iteration matrix representing the hybrid algorithm following different hybridization schemes is constructed. An analysis of the ei...

We present a computational study of the solution of the Falkner-Skan equation (a thirdorder boundary value problem arising in boundary-layer theory) using high-order and high-order-compact finite differences schemes. There are a number of previously reported solution approaches that adopt a reduced-order system of equations, and numerical methods such as: shooting, Taylor series, Runge-Kutta an...

Two-dimensional reactive Navier-Stokes equations are solved using a simple implicit Beam-Warming finite difference scheme. Comparisons of the detonation wave solutions of reactive Euler equations and reactive Navier-Stokes equations show that physical diffusion is important at high resolution when the numerical diffusion becomes negligible. Hence, for accurate detonation wave solutions it is ne...

We develop a two-dimensional solver for the acoustic wave equation with spatially varying coefficients. In what is a new approach, we use a basis of approximate prolate spheroidal wavefunctions and construct derivative operators that incorporate boundary and interface conditions. Writing the wave equation as a first-order system, we evolve the equation in time using the matrix exponential. Comp...

We present a domain decomposition solver for the 2D Helmholtz equation, with a special choice of integral transmission condition that involves polarizing the waves into oneway components. This refinement of the transmission condition is the key to combining local direct solves into an efficient iterative scheme, which can then be deployed in a highperformance computing environment. The method i...

Many different methods can be used to treat open boundary conditions in lattice Boltzmann method. Zou-He method, finite difference velocity gradient method, and regularized method are reviewed and compared for velocity Dirichlet condition for Poiseuille flow with different Reynolds numbers. Using same convergence criterion, all the numerical procedures are carried on till steady-states are reac...