Introduction Large friction and low Mach regimes Numerical strategy Numerical results

All-regime Lagrangian-Remap numerical schemes for the gas dynamics equations. Applications to the large friction and low Mach regimes Christophe Chalons LMV, Universit´e de Versailles Saint-Quentin-en-Yvelines

Joint works with M. Girardin and S. Kokh

1/63

Christophe Chalons

All-regime Lagrangian-Remap numerical schemes

2/63

Introduction Large friction and low Mach regimes Numerical strategy Numerical results

Outline

1

Introduction

2

Large friction and low Mach regimes

3

Numerical strategy

4

Numerical results

Christophe Chalons

All-regime Lagrangian-Remap numerical schemes

3/63

Introduction Large friction and low Mach regimes Numerical strategy Numerical results

Outline

1

Introduction

2

Large friction and low Mach regimes

3

Numerical strategy

4

Numerical results

Christophe Chalons

All-regime Lagrangian-Remap numerical schemes

Introduction Large friction and low Mach regimes Numerical strategy Numerical results

Introduction Motivation : numerical study of two-phase flows in nuclear reactors We consider the following model ∂t ρ + ∇ · (ρu) = 0 ∂t (ρu) + ∇ · (ρu ⊗ u) + ∇p = 0 ∂t (ρE ) + ∇ · [(ρE + p)u] = 0 where ρ, u = (u, v )t , E denote respectively the density, the velocity vector and the total energy of the fluid. Let e = E −

4/63

|u|2 2

be the specific and τ = 1/ρ the covolume

Christophe Chalons

All-regime Lagrangian-Remap numerical schemes

Introduction Large friction and low Mach regimes Numerical strategy Numerical results

Introduction We are especially interested in the design of numerical schemes when the model depends on a parameter  > 0 in the following three flow regimes Classical regime :  = O(1) Low  regime :