NKONGA , Boniface

We are concerned with the conservative approximations of compressible flows in the context of moving mesh or interface tracking. This paper makes a review of some numerical approaches, based on the Geometrical Conservation Law (GCL) property, for computation with moving mesh or moving boundary. Those methods are reformulated and some...

Our aim was to derive new models and numerical strategies for shear shallow flows on curved topography. This modeling was supported by physical and numerical experiments, investigations and validations. The initial scientific plan was organized in seven tasks. We will reconsider the initial tasks and gives some detail of the achievements of the...

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The shear shallow water model is a higher order model for shallow flows which includes some shear effects that are neglected in the classical shallow models. The model is a non-conservative hyperbolic system which can admit shocks, rarefactions, shear and contact waves. The notion of weak solution is based on a path but the choice of the...

Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting...

The understanding of Magnetohydrodynamic (MHD) instabilities is quite essential for the optimization of magnetically confined plasma. For example, the ITER (International Thermonuclear Experimental Reactor) scenario is expected to generate oscillations in the plasma core, modes around the outward limit of the plasma confinement zone, or local...

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In this paper are analyzed finite element methods based on Powell-Sabin splines, for the solution of partial differential equations in two dimensions. PS splines are piecewise quadratic polynomials defined on a triangulation of the domain, and exhibit a global C 1 continuity. Critical issues when dealing with PS splines, and described in this...

When high Reynolds turbulent flows are combined with complex and large size geometries, computers are no longer enough powerful to deal with Direct Numerical Simulation (DNS) and with the resolution of all the scales of turbulence motion. Therefore, the RANS approaches solve averaged equations and use a model to simulate these scales. This...

We are concerned with the numerical approximation of an incompressible ionized gas (plasma) flowing in a toroidal geometry. We also assume that the flow is independent of the toroidal coordinate and the resulting model is thus 2-D. We consider a symmetric formulation, the so-called Reduced Resistive MHD model, where the governing equation gives...

When high Reynolds turbulent flows are combined with complex and large size geometries, computers are no longer enough powerful to deal with Direct Numerical Simulation (DNS) and with the resolution of all the scales of turbulence motion. Therefore, at a fixed scale suitable for reasonable computations cost, the unresolved scales of the...

In the last recent years, thanks to the increasing power of the computational machines , the interest in more and more accurate numerical schemes is growing. Methods based on high-order approximations are nowadays the common trend in the computational research community, in particular for CFD applications. This work is focused on Powell-Sabin...

The majority of fluid flows that are interesting from a practical point of view are turbulent flows. The problem is that turbulence is particulary difficult to model. Although simulation of turbulent flows has been the topic of important researches, it remains an open issue. We present a stabilized finite element method combine with the one...

Diffuse interface methods with compressible fluids, considered through hyperbolic multiphase flow models, have demonstrated their capability to solve a wide range of complex flow situations in severe conditions (both high and low speeds). These formulations can deal with the presence of shock waves, chemical and physical transformations, such...

We derive a simple method to numerically approximate the solution of the two-dimensional Riemann problem for gas dynamics, using the literal extension of the well-known HLL formalism as its basis. Essentially, any strategy attempting to extend the three-state HLL Riemann solver to multiple space dimensions will by some means involve a piecewise...

We report on our study aimed at deriving a simple method to numerically approximate the solution of the two-dimensional Riemann problem for gas dynamics, using the literal extension of the well-known HLL formalism as its basis. Essentially, any strategy attempting to extend the three-state HLL Riemann solver to multiple space dimensions will by...

Many astrophysical flows are modeled by the Euler equations with gravity source terms derived from a potential, the evolution of which is described by a Poisson equation. Several gravitational flows reach equilibrium states that are necessary to preserve in the numerical formulation. In this paper, we present the derivation of the relaxation...

In this work, we use a stabilized finite element method to solve Spalart-Allmaras turbulent model for compressible flows. This method is the Streamline-Upwind Petrov-Galerkin one, which enable to put numerical viscosity only along the streamlines. The aim is to build a high order scheme in order not to pollute turbulent eddy viscosity with the...

Over the last 50 years several sediment transport models in coastal environments based on Shallow Water(SW) type models have been developed in the literature. The water flow over an abrupt moving topography quickly spatially variable becomes accelerated and strongly varied arising the turbulence (distortion). The acceleration and strong...

A flow model is built to capture evaporating interfaces separating liquid and vapour. Surface tension, heat conduction, Gibbs free energy relaxation and compressibility effects are considered. The corresponding flow model is hyperbolic, conservative and in agreement with the second law of thermodynamics. Phase transition is considered through...

The conduit equation is a dispersive non-integrable scalar equation modeling the flow of a low-viscous buoyant fluid embedded in a highly viscous fluid matrix. This equation can be written in a special form reminiscent of the famous Godunov form proposed in 1961 for the Euler equations of compressible fluids. We propose a hyperbolic...

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