Radial Basis Functions - Finite Difference (RBF-FD) Framework To Solve The Transport Equation In Environmental Modeling

In this project, a proposal for a framework to use the local radial basis functions (RBFs) method to approximate solutions for variations of the transport equation is introduced. The approach is also called the Radial Basis Functions - Finite Difference (RBF-FD) method. We discuss the difficulties of the method while also introducing solutions to resolve some of the issues that arise. The approach was used to solve the 1D transport equation that models contaminant water transport in a semi-infinite domain. Furthermore, the RBF-FD method was also used to solve the transport equation when decay and degradation are present in the problem with both finite and infinite domains. We then observed that the RBF-FD numerical approach gives high-accuracy approximations of the solutions transport equation up to machine accuracy.