Computer Assisted Numerical Methods with Animation Technology

The book consists literature survey on Darcy-Brinkman-Forchheimer flow and heat transfer equations and Bénard-Marangoni and Bénard-Darcy convection problems. Next is approximate solution of the Darcy-Brinkman-Forchheimer (DBF) flow equation using a combination of finite difference and homotopy continuation (HCM) method. DBF flows are considered in a porous channel, tube and annulus. The algorithm developed for the solution of the DBF equation succeeds in obtaining the flow velocity accurately up to 12 decimal digits. It is found that time complexity of the algorithm for the considered computer system, programming language, GCC compiler and memory is O(n3). A detailed analysis is made regarding optimal number of equations required for each set of parameters' values, for a convergent solution. Comparison is made between the results of the problem with that obtained using shooting method (Runge-Kutta-Fehlberg (RKF-45).