Higher order compact flowfield-dependent variation (HOC-FDV) method for one-dimensional viscous flow - M Elfaghi, Abdulhafid (Penerbit UTHM, 2020)
A higher order compact flowfield dependent variation (HOC-FDV) method, has been developed to solve Navier-Stokes equations. The flowfield-dependent variation (FDV) theory originally developed by expanding the conservative governing equations into a special form of Taylor series in terms of the flow field–dependent variation parameters as a function of flowfield primitive variables. The numerical scheme then guided by these parameters calculated between adjacent nodal points. In order to achieve higher order accuracy differentiation, the first and second order derivatives in the FDV equations are approximated by using the implicit high order compact differencing scheme involving a three-point stencil. This results in a higher order compact flowfield dependent variation (HOC-FDV) method which has a third-order accuracy in time and fourth-order accuracy in space. One-dimensional viscous nonlinear Burger's equation is solved as a study case to demonstrate the accuracy, and convergence characteristics of the higher-resolution scheme. Results obtained are compared with the exact and other numerical methods. Based on the results, it could be concluded that the HOC-FDV method is more accurate compared with the other approaches and the resolution power of the scheme is superior to that of conventional second-order schemes. FDV-HOC method is more efficient than second-order methods as less number of grid points can be used to obtain the same accuracy.