Modelling the motion of a cell population in the extracellular matrix

The paper aims at describing the motion of cells in fibrous tissues taking into account of the interaction with the network fibers and among cells, of chemotaxis, and of contact guidance from network fibers. Both a kinetic model and its continuum limit are described

Waves in Materials with Microstructure: Numerical Simulation

Results of numerical experiments are presented in order to compare direct numerical calculations of wave propagation in a laminate with prescribed properties and corresponding results obtained for an effective medium with the microstructure modelling. These numerical experiments allowed us to analyse the advantages and weaknesses of the microstructure model

Numerical Simulation of Waves and Fronts in Inhomogeneous Solids

Dynamic response of inhomogeneous materials exhibits new effects, which often do not exist in homogeneous media. It is quite natural that most of studies of wave and front propagation in inhomogeneous materials are associated with numerical simulations. To develop a numerical algorithm and to perform the numerical simulations of moving fronts we need to formulate a kinetic law of progress relating the driving force and the velocity of the discontinuity. The velocity of discontinuity is determined by means of the non-equilibrium jump relations at the front. The obtained numerical method generalizes the wave-propagation algorithm to the case of moving discontinuities in thermoelastic solids

Numerical modeling of two-phase gravitational granular flows with bottom topography

(A. Mangeney), [email protected] (J.-P. Vilotte). Summary. We study a depth-averaged model of gravity-driven mixtures of solid grains and fluid moving over variable basal surface. The particular application we are interested in is the numerical description of geophysical flows such as avalanches and debris flows, which typically contain both solid material and interstitial fluid. The depth-averaged mass and momentum equations for the solid and fluid components form a non-conservative system, where non-conservative terms involving the derivatives of the unknowns couple together the sets of equations of the two phases. The system can be shown to be hyperbolic at least when the difference of velocities of the two constituents is sufficiently small. We numerically solve the model equations in one dimension by a finite volume scheme based on a Roe-type Riemann solver. Well-balancing of topography source terms is obtained via a technique that includes these contributions into the wave structure of the Riemann solution

High-resolution Wave Propagation Method for Stratified Flows

The implementation of the multidimensional f-waves Riemann solver for the time-dependent, three-dimensional, nonhydrostatic, meso- and microscale atmospheric flows is described in detail. The Riemann solver employs flux-based wave decomposition (f-waves) for the calculation of Godunov fluxes in which the flux differences are written directly as the linear combination of the right eigenvectors of the hyperbolic system. The scheme incorporates the source term due to gravity without introducing discretization errors which is an important property in the context of atmospheric flows. The resulting flow solver is conservative, accurate, stable, and well-balanced. The implementation of the solver is evaluated using benchmark test cases for atmospheric dynamics