A new numerical algorithm based on transformed equations and its applications to very low Re fluid flows

A new numerical algorithm is presented in this study to solve the partial differential equations that govern fluid flows. This new algorithm is based on first transforming the partial differential equations by introducing an exponential function to eliminate the convection terms. A fourth-order central differencing scheme and a second-order central differencing scheme are used to discretize the transformed equations. The algorithm is then applied to simulate fluid flows with exact solutions to validate this new algorithm. The fluid flows used in this study are a self-designed quasi-fluid flow problem, stagnation in plane flow (Hiemenz flow), and flow between two concentric cylinders. Comparisons against the exact solution are made for the results obtained using the new numerical algorithm as well as the power-law scheme. The comparisons indicate that the present fourth-order scheme performs the best and the present second-order scheme is the next most accurate.