This paper constructs extrapolated implicit-explicit time stepping methods that allow one to efficiently solve problems with both stiff and nonstiff components. The proposed methods are based on Euler steps and can provide very high order discretizations of ODEs, index-1 DAEs, and PDEs in the method of lines framework. Implicit-explicit schemes based on extrapolation are simple to construct, ea...

The work focuses on the development of a 2D quadrilateral element based Spectral Difference solver for viscous flow calculations, and the application of the p-multigrid method and implicit time-stepping to accelerate convergence. This paper extends the previous work by Liang et al (2009) on the p-multigrid method for 2D inviscid compressible flow, to viscous flows. The high-order spectral diffe...

In the context of nonlinear conservation laws a model for multiphase flows where slow kinematic waves co-exist with fast acoustic waves is discretized with an implicit-explicit time scheme. Space adaptivity of the grid is implemented using multiresolution techniques and local time stepping further enhances the computing time performances. A parametric study is presented to illustrate the robust...

We make an initial investigation into the temporal efficiency of a fully discrete summation-by-parts approach for stiff unsteady flows with boundary layers. As a model problem for the Navier-Stokes equations we consider a two-dimensional advection-diffusion problem with a boundary layer. The problem is discretized in space using finite difference approximations on summation-by-parts form togeth...

We present a fully adaptive numerical scheme for evolutionary PDEs in Cartesian geometry based on a second-order finite volume discretization. A multiresolution strategy allows local grid refinement while controlling the approximation error in space. For time discretization we use an explicit Runge–Kutta scheme of second-order with a scale-dependent time step. On the finest scale the size of th...

[1] Physics‐based global magnetosphere modeling requires large computational resources. It is still impractical to resolve the computational domain to the point where numerical errors become negligible. One possible way of reducing numerical diffusion is the “Boris correction”: the semirelativistic magnetohydrodynamics equations are solved with an artificially reduced speed of light. Here we in...

In the current work, a fully implicit numerical integration scheme is developed for modeling twinning-induced plasticity using crystal framework. Firstly, constitutive formulation of twin-based micromechanical model presented to estimate deformation behavior steels with low stacking fault energy. Secondly, discretizing equations through time backward Euler method. A sub-stepping algorithm and t...

A 2D Navier-Stokes solver was developed to simulate steady,laminar flow over a backward-facing step of height h. The step expansion ratio=1/2 and the flow at the step was assumed to be fully developed, laminar channel flow. The Reynolds number for this flow was defined as Re=Uh/ν. The 2D incompressible Navier-Stokes equations was solved in generalized curvilinear coordinates using artificial co...

in this paper the numerical simulation and operation comparison of two sizes of air gun pellets with 4.5 and 5.5 mm calibers is performed. these pellets affected by drag force and are encountered to continuous velocity variations and experience an unsteady flow. in order to solve this problem numerically, the navier- stokes equations in an unsteady compressible turbulent flow with the dynamical...

A new horizontally explicit/vertically implicit (HEVI) time splitting scheme for atmospheric modelling is introduced, which the horizontal divergence terms are applied within vertical substep. The HEVI implemented in conjunction with a mixed mimetic spectral element spatial discretisation and semi-implicit stepping that both preserve skew-symmetric structure of non-canonical Hamiltonian form eq...