Multispecies

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Multispecies approach implemented in the code is based on the paper "Multi-species Lattice Boltzmann Model and Practical Examples. Short Course material Pietro Asinari PhD."

Equlibrium distribution function for multispecies is given in the paper as

where, for and , is molecular weight for species .

is given as

Relaxation time is given as

Multispecies: Variable Transformation

A semi-implicit Lattice Boltzmann equation is given as,

Variable transformation presented in above paper involves three steps

Step 1. Transforming f -> g

Step 2. Stream and Collide i.e g -> g^+

Step 3. Back Transormation to f i.e g^+ -> f^+

In back tranformation, to compute feq we need and can be computed directly from g

where as the computed by solving the linear system of equation given below

where, is,

       !West
       u_n(1) = - uxstar(s)
       !south
       u_n(2) =             - uystar(s)
       !bottom
       u_n(3) =                         - uzstar(s)
       !east
       u_n(4) =   uxstar(s)
       !north
       u_n(5) =               uystar(s)
       !top
       u_n(6) =                           uzstar(s)
       !bottom south
       u_n(7)
       !top south
       u_n(7)
       !bottom north
       u_n(7)
       !top north
       u_n(7)
       !bottom west
       u_n(7)
       !bo
       u_n(7)
       u_n(7)
       u_n(7)
       u_n(7)

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