A novel time integration approach is explored for unsteady flow computations. It is a multi-block formulation in time where one solves for all time levels within a block simultaneously. The time discretization within a block is based on the summation-by-parts (SBP) technique in time combined with the simultaneous-approximation-term (SAT) technique for imposing the initial condition. The approac...

Solving an evolution problem in parallel is naturally undertaken by trying to parallelize the algorithm in space, and then still follow a time stepping method from the initial time t = 0 to the final time t = T . This is especially easy to do when an explicit time stepping method is used, because in that case the time step for each component is only based on past, known data, and the time stepp...

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fo...

in this paper we investigate a nonlinear evolution model described by the rosenau-kdv equation. we propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of o(τ2 + h2). furthermore we show the existence and uniqueness of numerical solutions. comparing the numerical results with other methods in...

We consider an unfitted Eulerian time-stepping scheme for a coupled parabolic model problem on moving domain. In this model, the domain motion results from ordinary differential equation to bulk via forces acting interface. extend our initial work (von Wahl & Richter, 2022) allow equal-order finite element discretisations partial and Lagrange multiplier spaces. Together with BFD2 scheme, lowest...

In this paper, we are interested in the numerical approximation of the classical time-dependent drift-diffusion system near quasi-neutrality. We consider a fully implicit in time and finite volume in space scheme, where the convection-diffusion fluxes are approximated by ScharfetterGummel fluxes. We establish that all the a priori estimates needed to prove the convergence of the scheme does not...

We study solution techniques for parabolic equations with fractional diffusion and Caputo fractional time derivative, the latter being discretized and analyzed in a general Hilbert space setting. The spatial fractional diffusion is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem posed on a semi-infinite cylinder in one more spatial dimension. We write our evolution ...

IMEX partitioning may be based on a decomposition of the computational domain into two subgrids by implicitly discretizing unknowns smallest cells while explicit time stepping is applied to moderately sized elements. Alternatively, advection-diffusion splitting applies implicit discretization only viscous terms inviscid are discretized explicitly. Analytical investigations have shown that caref...

The one-fluid visco-resistive MHD model provides a description of the dynamics of a charged fluid under the influence of an electromagnetic field. This model is strongly coupled, highly nonlinear, and characterized by physical mechanisms that span a wide range of interacting time scales. Solutions of this system can include very fast component time scales to slowly varying dynamical time scales...

This paper describes the implementation of a solver for systems of semi-linear parabolic partial di erential equations in two and three space dimensions. The solver is based on a parallel implementation of a non-linear Alternating Direction Implicit (ADI) scheme which uses a Cartesian grid in space and an implicit time-stepping algorithm. Various reordering strategies for the linearized equatio...