Abstract The purpose of this work is to study an example of low Mach (Froude) number limit of compressible flows when the initial density (height) is almost equal to a function depending on x. This allows us to connect the viscous shallow water equation and the viscous lake equations. More precisely, we study this asymptotic with well prepared data in a periodic domain looking at the influence ...

Many applied time-dependent problems are characterized by an additive representation of the problem operator. Additive schemes are constructed using such a splitting and associated with the transition to a new time level on the basis of the solution of more simple problems for the individual operators in the additive decomposition. We consider a new class of additive schemes for problems with a...

The dynamics of the growth of linear disturbances to a chaotic basic state is analyzed in an asymptotic model of weakly nonlinear, baroclinic wave-mean interaction. In this model, an ordinary differential equation for the wave amplitude is coupled to a partial differential equation for the zonal flow correction. The leading Lyapunov vector is nearly parallel to the leading Floquet vector φ1 of ...

We consider a prototype two-phase uid-ow model with capillary forces. The pressure equation is solved using standard nite-elements and multigrid techniques. The parabolic saturation equation is addressed via a novel corrected operator splitting approach. In typical applications, the importance of advection versus diiusion (capillary forces) may change rapidly during a simulation. The corrected ...

Steady state axisymmetric deformations of a homogeneous, isotropic, compressible and rigid perfectly plastic target being penetrated by a rigid cylindrical penetrator with a hemispherical nose are studied by the finite element method. The steady state is reached with respect to an observer situated on the penetrator nose and moving with it. Tillotson’s equation, restricted to mechanical deforma...

Contents Introduction 5 Chapter 1. The theory in the smooth framework 11 1.1. The ordinary differential equation 11 1.2. Existence and uniqueness in the classical setting 11 1.3. The classical flow of a vector field 16 1.4. The transport equation and the continuity equation 19 Part 1. The Eulerian viewpoint 23 Chapter 2. Renormalized solutions and well-posedness of the PDE 25 2.1. A strategy to...

We focus on mono-dimensional hyperbolic systems approximated by a particular lattice Boltzmann scheme. The scheme is described in the framework of the multiple relaxation times method and stability conditions are given. An analysis is done to link the scheme with an explicit finite differences approximation of the relaxation method proposed by Jin and Xin. Several numerical illustrations are gi...

This paper presents a general overview of ow in deformable porous media with emphasis on melt extraction processes beneath mid-ocean ridges. Using a series of simple model problems, we show that the equations governing magma migration have two fundamentally different modes of behaviour. Compressible two-phase ow governs the separation of melt from the solid and forms a non-linear wave equation ...

Approximate solutions of the Fisher equation obtained by different splitting methods are investigated. The error of this nonlinear problem is analyzed. The order of different splitting methods coupled with numerical methods of different order is calculated numerically and symbolically.