Asymptotic Stability of a 9-point Multigrid Algorithm for Convection-diffusion Equations∗

Asymptotic Stability of a 9-point Multigrid Algorithm for the Convection-Diffusion Equations

Incremental unknowns method based on the theta-scheme for time-dependent convection-diffusion equations

A θ-scheme using two-level incremental unknowns is presented for solving time-dependent convection–diffusion equations in two-dimensional case. The IMG algorithm (Inertial Manifold–Multigrid algorithm) including the second-order incremental unknowns is convergent. The incremental unknowns method based on the θ-scheme needs a stability condition as 0 ≤ θ < 1/2 and is unconditionally stable as 1/...

Numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type

In this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

A Compact Multigrid Solver for Convection-Diffusion Equations

diffusion equations using a nine-point compact difference scheme. implementation with multigrid, and carry out a Fourier We test the efficiency of the algorithm with various smoothers and smoothing analysis of the Gauss–Seidel operator. In Secintergrid transfer operators. The algorithm displays a grid-indepention 3 we present numerical experiments that demonstrate dent convergence rate and prod...

High Accuracy and Scalable Multiscale Multigrid Computation for 3D Convection Diffusion Equation

We present a sixth order explicit compact finite difference scheme to solve the three dimensional (3D) convection diffusion equation. We first use multiscale multigrid method to solve the linear systems arising from a 19-point fourth order discretization scheme to compute the fourth order solutions on both the coarse grid and the fine grid. Then an operator based interpolation scheme combined w...