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With a new set of modified vorticity boundary conditions, we obtain agreement between the primitive variable and stream function-vorticity solutions.
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This paper presents an alternative formulation to the primitive variable form of the Navier-Stokes equations.
The primitive variable Newton's method converges much faster than the other two methods.
The primitive variable interpolation is, therefore, considered to be better choice for compressible multicomponent flows in the framework of WCNS.
After that, a single conversion from the conserved to the primitive variable is needed in each cell.
The variable property Navier-Stokes equation expressed in terms of the primitive variable velocity and pressure is solved with the mass continuity and temperature equations.
Then, a second WENO reconstruction is performed on the point values of the primitive variables to obtain piecewise high order reconstruction polynomials of the primitive variables.
The degrees of freedom are only the primitive variables: displacements and rotations at the nodes.
The primitive variables are represented pseudospectrally (Fourier in the stream- and spanwise directions, Chebyshev wall-normal).
Also used are sequences of nonuniform, staggered grids for the primitive variables.
The primitive variables, ϕ, u i, T, are continuous functions in space and time.
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