Abstract

Abstract

To evaluate the computational performance of high-order elements, a comparison based on operation count is proposed instead of runtime comparisons. More specifically, linear versus high-order approximations are analyzed for implicit solver under a standard set of hypotheses for the mesh and the solution. Continuous and discontinuous Galerkin methods are considered in two-dimensional and three-dimensional domains for simplices and parallelotopes. Moreover, both element-wise and global operations arising from different Galerkin approaches are studied. The operation count estimates show, that for implicit solvers, high-order methods are more efficient than linear ones.

Abstract

In this study, an implicit algorithm and different solvers are applied to the Moving Particle Semi-Implicit (MPS) method for temperature calculation. The original MPS method uses an explicit method for temperature calculation and is limited by time increment due to diffusion number. In this paper, the heat conduction of plates with Dirichlet boundary condition and Neumann boundary condition is studied. The accuracy of explicit and implicit calculation of plate heat transfer cases are compared. In addition, different solvers are compared. Consequently, it is shown thatthe error of the implicit algorithm is not much different from the original one. And CG is still the better solver,CGS is also a superior solver. The implicit algorithm increases the size of a single time stepby a maximum of 50 times (original diffusion number is 0.2), while the calculation time of a single time step does not increase Substantially, so it has a significant effect on the acceleration of calculation.

Abstract