This paper studies the error in, the efficient implementation of and time stepping methods for a variational multiscale method (VMS) for solving convectiondominated problems. The VMS studied uses a fine mesh C 0 finite element space Xh to approximate the concentration and a coarse mesh discontinuous vector finite element space LH for the large scales of the flux in the two scale discretization....

In this report, we propose a semi-implicit coupling scheme for the numerical simulation of fluid-structure interaction systems involving a viscous incompressible fluid. The scheme is stable irrespectively of the so-called addedmass effect and allows for conservative time-stepping within the structure. The efficiency of the scheme is based on the explicit splitting of the viscous effects and geo...

The push towards larger and larger computational platforms has made it possible for climate simulations to resolve climate dynamics across multiple spatial and temporal scales. This direction in climate simulation has created a strong need to develop scalable time-stepping methods capable of accelerating throughput on high performance computing. This work details the recent advances in the impl...

in this article we discussed the numerical solution of Burgers’ equation using multigrid method. We used implicit method for time discritization and Crank-Nicolson scheme for space discritization for fully discrete scheme. For improvement we used Multigrid method in fully discrete solution. And also Multigrid method accelerates convergence of a basics iterative method by global correction. Nume...

A fully implicit solver is developed for the mesoscale nonhydrostatic simulation of atmospheric flows governed by the compressible Euler equations. To spatially discretize the Euler equations on a height-based terrain-following mesh, we apply a cell-centered finite volume scheme, in which an AUSM-up method with a piecewise linear reconstruction is employed to achieve secondorder accuracy for th...

We apply a multigrid reduction-in-time (MGRIT) algorithm to hyperbolic partial differential equations in one spatial dimension. This study is motivated by the observation that sequential time-stepping is a computational bottleneck when attempting to implement highly concurrent algorithms, thus parallel-in-time methods are desirable. MGRIT adds parallelism by using a hierarchy of successively co...

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...

The immersed boundary method is known to exhibit a high degree of numerical sti ness, which is associated with the interaction of immersed elastic bres with the surrounding uid. We perform a linear analysis of the underlying equations of motion for immersed bres, and identify a discrete set of bre modes which are associated solely with the presence of the bre. These results are a generalisation...

Recently, the authors introduced a preconditioner for the linear systems that arise from fully implicit Runge-Kutta time stepping schemes applied to parabolic PDEs [9]. The preconditioner was a block Jacobi preconditioner, where each of the blocks were based on standard preconditioners for low-order time discretizations like implicit Euler or Crank-Nicolson. It was proven that the preconditione...