Power law scheme

The power law scheme was first used by Suhas Patankar (1980). It helps in achieving approximate solutions in computational fluid dynamics (CFD) and it is used for giving a more accurate approximation to the one-dimensional exact solution when compared to other schemes in computational fluid dynamics (CFD). This scheme is based on the analytical solution of the convection diffusion equation. This scheme is also very effective in removing False diffusion error.

The power-law scheme interpolates the face value of a variable, ${\displaystyle \phi \,}$, using the exact solution to a one-dimensional convection-diffusion equation given below:

In the above equation Diffusion Coefficient, ${\displaystyle \Gamma }$ and both the density ${\displaystyle \rho }$ and velocity remains constant u across the interval of integration.

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