User talk:Bossenne

Work in progress, come back later ! =)

Motivation

H-Allegro uses the compressible and reactive Navier-Stokes equations in order to solve two-phase combustion. It also takes into account a simplified chemistry of the reaction and the propagation of acoustic waves.

H-Allegro was developped by Eric Albin and Marianne Sjostrand.

Equations and Hypotheses

Equations

• ${\dfrac {\partial {\rho }}{\partial {t}}}+{\dfrac {\partial {{\rho }U_{j}}}{\partial {x_{j}}}}=0$

• ${\dfrac {\partial {{\rho }U_{i}}}{\partial {t}}}+{\dfrac {\partial {\rho }U_{i}U_{j}}{\partial {x_{j}}}}+{\dfrac {\partial {P}}{\partial {x_{i}}}}={\dfrac {\partial {\tau _{ij}}}{\partial {x_{j}}}}+S_{i}$

• ${\dfrac {\partial {{\rho }E}}{\partial {t}}}+{\dfrac {\partial {(P+{\rho }E)}U_{j}}{\partial {x_{j}}}}={\dfrac {\partial {q_{j}}}{\partial {x_{j}}}}+{\dfrac {\partial {\tau _{ij}U_{i}}}{\partial {x_{j}}}}+S_{5}$

• ${\dfrac {\partial {{\rho }Y_{k}}}{\partial {t}}}+{\dfrac {\partial {{\rho }Y_{k}U_{j}}}{\partial {x_{j}}}}={\dfrac {\partial {q_{j}^{k}}}{\partial {x_{j}}}}+S_{k}$

Hypotheses

Partie de Mélissa

Models

To do

Numerics

• Spatial : 6th-order finite difference scheme

• Temporal : 3rd order explicit time integration (Runge-Kutta3)

• Chemical : one step Arrhenius' law

• Boundary conditions : the 3D-NSCBC processing, applied in a referential attached to the local streamlines.