Study On Meshless Method With Radial Basis Functions For Two-flow Domain Model

In recent decades,preventing the soil environment from being polluted and soil salinization have been widely concerned by researchers from all over the world who have conducted a massive amount of research.Experts have specifically described the process of soil solute migration by establishing different mathematical models.Among them,the two-flow domain model is the most widely used.Yet owing to the unique coupling form and complicated boundary conditions of the governing equations of the two-flow domain model,it is challenging to find analytical solution of the basic equation of the model for researchers.Therefore,developing corresponding numerical methods to solve such equations is quite significant.Based on the above background,the radial basis meshless method is mainly used to resolve the one-dimensional and two-dimensional integer-order two-flow domain models and the time fractional two-flow domain model in this paper.Its main contents are divided into the following sections:(1)Introduce the research background,significance and status of integer-order two-flow domain model and time fractional two-flow domain model;Sort out and introduce the development history and research status of the radial basis meshless method,and the basic knowledge of radial basis function interpolation.Present Some basic theoretical knowledge of fractional calculus.(2)Aiming at the one-dimensional and two-dimensional integer-order two-flow domain model in solute motion process,the format derivation and numerical simulation of the radial basis meshless algorithm are carried out in the first place.In addition,it is concluded that the factors that affect the numerical calculation accuracy of the algorithm in this paper are not unique by analyzing the relationship between the calculated results and free parameters,the number of space nodes and time step.Finally,compared with the finite difference method,the accuracy of the numerical results in this paper is higher.(3)Relating to governing equations for one-dimensional and two-dimensional time fractional two-flow domain model,the discrete format of the governing equations of the one-dimensional and two-dimensional time fractional two-flow domain models in the sense of Caputo derivative is derived.Ultimately,comparing the algorithm with the finite difference method,the results of numerical examples show that the algorithm in this paper has more advantages in numerical calculation accuracy than the finite difference method.