A highly efficient parallelization scheme of direct numerical simulation (DNS) for two-dimensional Rayleigh-Bénard convection is presented. By introducing the parallel diagonal dominant (PDD) algorithm to solve the pressure Poisson equation and adjusting the domain decomposition accordingly, all-to-all communication as the usual obstacle to parallel computing can be eliminated. Excellent strong scaling and weak scaling for the parallel efficiency are achieved. Numerical results show that very complex structures in flow exist at very high Ra numbers. The required high resolution both in space and in time can be obtained by the present method at low parallel overhead.

Computational scientists generally seek more accurate results in shorter times, and to achieve this a knowledge of evolving programming paradigms and hardware is important. In particular, optimising solvers for linear systems is a major challenge in scientific computation, and numerical algorithms must be modified or new ones created to fully use the parallel architecture of new computers. Parallel space discretisation solvers for Partial Differential Equations (PDE) such as Domain Decomposition Methods (DDM) are efficient and well documented. At first glance, parallelisation seems to be inconsistent with inherently sequential time evolution, but parallelisation is not limited to space directions. In this article, we present a new and simple method for time parallelisation, based on partial fraction decomposition of the inverse of some special matrices. We discuss its application to the heat equation and some limitations, in associated numerical experiments.

This paper presents a relatively simple numerical method to investigate the flow and heat transfer of laminar power-law fluids over a semi-infinite plate in the presence of viscous dissipation and anisotropy radiation. On one hand, unlike most classical works, the effects of power-law viscosity on velocity and temperature fields are taken into account when both the dynamic viscosity and the thermal diffusivity vary as a power-law function. On the other hand, boundary layer equations are derived by Taylor expansion, and a mixed analytical/numerical method (a pseudosimilarity method) is proposed to effectively solve the boundary layer equations. This method has been justified by comparing its results with those of the original governing equations obtained by a finite element method. These results agree very well especially when the Reynolds number is large. We also observe that the robustness and accuracy of the algorithm are better when thermal boundary layer is thinner than velocity boundary layer.

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of convection-diffusion type of third order Ordinary Differential Equations (ODEs) in which the SPBVP is reduced into a weakly coupled system of two ODEs subject to suitable initial and boundary conditions. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. In order to get a numerical solution for the derivative of the solution, the domain is divided into two regions namely inner region and outer region. The shooting method is applied to the inner region while standard finite difference scheme (FD) is applied for the outer region. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing.

Many motion planning methods use Configuration Space to represent a robot manipulator's range of motion and the obstacles which exist in its environment. The Cartesian to Configuration Space mapping is computationally intensive and this paper describes how the execution time can be decreased by using parallel processing. The natural tree structure of the algorithm is exploited to partition the computation into parallel tasks. An implementation programmed in the occam2 parallel computer language running on a network of INMOS transputers is described. The benefits of dynamically scheduling the tasks onto the processors are explained and verified by means of measured execution times on various processor network topologies. It is concluded that excellent speed-up and efficiency can be achieved provided that proper account is taken of the variable task lengths in the computation.

A problem independent, equation decomposition scheme of parallel computation is adopted and tested using a two-dimensional turbulent channel flow. The incompressible Navier-Stokes equations, incorporated with the SIMPLEC algorithm and a two-layer turbulence model, were distributed to four nodes of IBM SP2 parallel machine using the PVM software and solved simultaneously. The computation domain and the interior iteration loop for the solution of every transport equation is the same, load balancing among different machines is automatically satisfied. Since all the transport equations and the flow field was solved and updated simultaneously, the solutions obtained from the equation decomposition scheme at each time step were more accurate than those obtained from a unit process code, which in turn sharply reduced the required convergence time steps. Without modifying any of the solution algorithm, or tuning the computer code, the rate of convergence speeds up more than four times by invoking four nodes of parallel machines using the equation decomposition scheme.