Flow Models

Three different compressible flow models are implemented in HAMeRS. They are respectively:

1. Single-species conservative model
2. Multi-species conservative model with isothermal and isobaric equilibrium assumptions
3. Multi-species quasi-conservative model with isobaric equilibrium assumption by Allaire et al.

In each of the models, there are respectively the Euler (inviscid) and Navier-Stokes (viscous) versions.

1. Single-Species Conservative Model

a. Euler Version

The governing equations are:

b. Navier-Stokes Version

The governing equations are:

The viscous stress tensor for Newtonian fluid is implemented:

The conductive flux is implemented as:

2. Multi-Species Conservative Model with Isothermal and Isobaric Equilibrium Assumptions

a. Euler Version

The governing equations are:

b. Navier-Stokes Version

The governing equations are:

The diffusive mass flux of each species is given by the Fickian diffusion approximation:

The viscous stress tensor for Newtonian fluid is implemented:

The conductive flux is implemented as:

The inter-species diffusional enthalpy flux suggested by Cook is given by:

3. Multi-Species Quasi-Conservative Model with Isobaric Equilibrium Assumption by Allaire et al.

a. Euler Version

The governing equations are:

b. Navier-Stokes Version

The governing equations are:

The viscous stress tensor for Newtonian fluid is implemented: