In this paper we generalize the degenerate two{phase Stefan problem (Mullins{ Sekerka evolution) to multi{phase systems. We prove a conditional existence result for this evolution problem in the framework of geometric measure theory by using an implicit time discretization. In each time step we solve a variational problem for an energy functional that contains capillarity terms as well as bulk ...

Abstract In this work, a method is put forward to obtain the dynamic solution efficiently and accurately for large-scale train–track–substructure (TTS) system. It called implicit-explicit integration multi-time-step (abbreviated as m I- n E-MTS method). The TTS system divided into train–track subsystem substructure subsystem. Considering that root cause of low efficiency obtaining lies in solvi...

We consider a fully discrete implicit nite element approximation of a model for phase separation of a multi-component alloy. We prove existence, uniqueness and stability of the numerical solution for a suuciently small time step. We prove convergence to the solution of the associated continuous problem. We perform a linear stability analysis of the equations and describe some numerical experime...

This paper is concerned with the solvability of implicit time-stepping methods for simulating the dynamics of multi-body systems. The standard approach is to select a time-step based on desired level of accuracy and computational efficiency of integration. Implicit methods impose an additional but often overlooked requirement that the resulting nonlinear root-finding problem is solvable and has...

In numerical time-integration with implicit-explicit (IMEX) methods, a within-step adaptable decomposition called residual balanced decomposition is introduced. This decomposition allows any residual occurring in the implicit equation of the implicit-step to be moved into the explicit part of the decomposition. By balancing the residual, the accuracy of the local truncation error of the time-st...

Implicit pressure-explicit saturation method (IMPES) is widely used in oil reservoir simulation to study the multiphase flow in porous media. This method has no complexity compared to the fully implicit method, although both of them are based on the finite difference technique. Water coning is one the most important phenomenon that affects the oil production from oil reservoirs having a water d...

We describe a sequential fully implicit (SFI) multi-scale finite volume (MSFV) algorithm for nonlinear multi-phase flow and transport in heterogeneous porous media. The method extends the recently developed multiscale approach, which is based on an IMPES (IMplicit Pressure, Explicit Saturation) scheme [P. Jenny, S.H. Lee, H.A. Tchelepi, Adaptive multiscale finite volume method for multi-phase f...

In this paper we review and further develop a class of strong-stability preserving (SSP) high-order time discretizations for semi-discrete method-of-lines approximations of partial di erential equations. Termed TVD (total variation diminishing) time discretizations before, this class of high-order time discretization methods preserves the strong-stability properties of rst-order Euler time step...