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, formula_1, using the exact solution to a one-dimensional convection-diffusion equation given below:  In the above equation Diffusion Coefficient, formula_3 and both the density formula_4 and velocity remains constant u across the interval of integration. Integrating the equation, with Boundary Conditions,  Variation of face value with distance, x is given by the expression, formula_7  where Pe is the Peclet number given by formula_8  Peclet number is defined to be the ratio of the rate of convection of a physical quantity by the flow to the rate of diffusion of the same quantity driven by an appropriate gradient. The variation between formula_1 and x is depicted in Figure for a range of values of the Peclet number. It shows that for large Pe, the value of formula_1 at x=L/2 is approximately equal to the value at upwind boundary which is assumption made by the upwind differencing scheme. In this scheme diffusion is set to zero when cell Pe exceeds 10. This implies that when the flow is dominated by convection, interpolation can be completed by simply letting the face value of a variable be set equal to its ``upwind" or upstream value. When Pe=0 (no flow, or pure diffusion), Figure shows that solution, formula_1 may be interpolated using a simple linear average between the values at x=0 and x=L. When the Peclet number has an intermediate value, the interpolated value for formula_1 at x=L/2 must be derived by applying the ``power law" equivalent. The simple average convection coefficient formulation can be replaced with a formula incorporating the power law relationship :  where formula_13  Fl,Dl and Fr,Dr are the properties on the left node and right node respectively. The central coefficient is given by ac=al+ar+(Fr-Fl)  Final coefficient form of the discrete equation: formula_14