Balancing Domain Decomposition for Non-stationary Incompressible Flow Problems Using a Characteristic-curve Method

Abstract

Numerical solutions for large scale models face the problem of poor convergence and for non-stationary problems the situation becomes worse. To speed up the convergence, an algorithm to perform the Balancing Domain Decomposition (BDD) preconditioning for non-stationary incompressible flow problems is constructed. The problem caused by the presence of nonlinear convection term in the non-stationary Navier-Stokes equations, which complicates the solving of the equations numerically, is solved by a characteristic-curve method. The method is advantageous as it renders the matrix for linear equations symmetric, thus enabling the Conjugate Gradient (CG) method to be used to solve the interface problem of the Domain Decomposition Method (DDM). The related algorithms are all implemented in parallel by the Hierarchical Domain Decomposition Method (HDDM) and the program has the capability of solving non-stationary problems with up to 10 million degrees of freedom (DOF). The BDD algorithm together with characteristic-curve method is applied to a benchmark problem, a three-dimensional driven cavity flow model, and the results are compared with available solutions.

Large Scale Simulation of Hydrogen Dispersion by a Stabilized Balancing Domain Decomposition Method

“…As can be seen from (24) and (25), the concentration expansion coefficient keeps approximately independent of with the parameters given in Table 1. This finding makes it very convenient to apply the current solver to simulate the hydrogen dispersion behaviour.…”

“…where is the Schur complement, is the interface degrees of freedom, and is the relative RHS vector [16,24]. The Neumann-Neumann preconditioner might be a popular choice for domain decomposition preconditioning [18,25], as the original local Schur complement can be conveniently used as the local operator. However, it shows its drawback of lacking of mechanism to exchange information between subdomains, because of the singularities caused by the floating subdomains.…”

A Pressure-Stabilized Lagrange-Galerkin Method in a Parallel Domain Decomposition System

“…However, the number of total elements in one subdomain may be different, which means that some point to point communication techniques, such as MPI Send/MPI Recv or MPI Sendrecv in MPICH, cannot be used in element wise computation. In the previous research [23], a global variable to store all the old solutions is constructed. This method maintains a high computation speed but costs a huge memory usage.…”

Numerical Simulation of the Hydrogen Dispersion Behavior by a Parallel Characteristic Curve Method

“…The number of total elements in one subdomain may be different, which means that some point to point communication techniques, such as MPI Send/MPI Recv or MPI Sendrecv in MPICH, cannot be used in elementwise computation. In the previous research [17], a global variable to store all the old solutions is constructed. This method maintains a high computation speed but costs a huge memory usage.…”