In this paper we study the stability for all positive time of the fully implicit Euler scheme for the two-dimensional Navier–Stokes equations. More precisely, we consider the time discretization scheme and with the aid of the discrete Gronwall lemma and the discrete uniform Gronwall lemma we prove that the numerical scheme is stable.

A fully implicit, fully adaptive multigrid method for the simulation of free dendritic growth into an undercooled melt has been developed and applied to various phase-field models. The main aim of this work is to demonstrate that advanced numerical methods, such as mesh adaptivity, implicit time stepping, multigrid methods and variable time step control, are not only advantageous compared to wi...

ABSTRACT This study presents an investigation of the interaction effect of one loaded pile on a neighboring pile under transient dynamic loadings. Analyses are carried for non homogeneous soils. The hybrid boundary element formulation is used to represent boundary integral representation of soil domain and pile equations represented by linear structural components. The formulation is presented ...

Reaction-Advection-Diffusion problems occurring in Air Pollution Models have very stiff reaction terms and moderately stiff vertical mixing (diffusion and cloud transport) terms which both should be integrated implicitly in time. Standard implicit time stepping is by far too expensive for this type of problems whereas widely used splitting techniques may lead to unacceptably large errors for fa...

We propose here a numerical scheme to compute the motion of rigid bodies with a non-elastic impact law. The method is based on a global computation of the reaction forces between bodies. Those forces, whose direction is known since we neglect friction effects, are identified at the discrete level with a scalar which plays the role of a Kuhn-Tucker multiplier associated to a first-order approxim...

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...

Macopa is a partial differential equations solver based on a particular local time stepping technique dedicated to multi-physics and multi-scale problems. Here, some parallelisation strategies – multithreading, domain decomposition, and hybrid OpenMP/MPI– are introduced for this solver. Their efficiency is evaluated on a few examples. 1 Context Numerical simulation has become a central tool for...

In this paper, we provide a convergence analysis of a projection semi-implicit scheme for the simulation of fluid-structure systems involving an incompressible viscous fluid. The error analysis is performed on a fully discretized linear coupled problem: a finite element approximation and a semiimplicit time-stepping strategy are respectively used for space and time discretization. The fluid is ...

Recently, we have proposed a method for solving steady-state convection-diffusion equations, including the full compressible Navier-Stokes equations [17]. The method is a combination of a mixed Finite Element method for the diffusion terms, and a Discontinuous Galerkin method for the convection term. The method is fully implicit, and the globally coupled unknowns are the hybrid variables, i.e.,...