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

The theory and numerical solutions of partial differential equations have been researched and applied in different fields with the continuous progress and development of technology and society.Scholars at home and abroad have specrfically described the characteristics of soil pore velocity by establishing different mathematical models.How to improve the numerical method to solve the two-flow domain model has become a research trend in academia.This paper mainly considers the two-flow domain model and the time-fractional two-flour domain model,and combines the ridge basis function with the collocation method to propose the meshless method with ridge basis functions.The main work is as follows:(1)The background significance and research status of the two-flow domain model as well as the time fractional two-flow domain model are introduced.The research progress and related theories of the ridge basis meshless method are generalized.And some basic theoretical knowledge of fractional calculus are given.(2)Aiming at the basic equations of the one-dimensional and two-dimensional two-flow domain models,the effective ridge basis meshless algorithm formats are first constructed,respectively.That is,the approximate function is constructed by the ridge basis function,and the control equation is dispersed using the collocation method.And then the existence and uniqueness of numerical solutions are analyzed.At last,numerical examples are given to discuss the influencing factors of the ridge basis meshlcss method and compare the proposed method with the finite difference method(FDM).The numerical results show that the meshless method with ridge basis functions is more advantageous in terms of the calculation accuracy and convergence.(3)For the solution of the basic equations of the one-dimensional and two-dimensional time fractional two-flow domain models,the ridge basis meshless algorithm formats based on L1 interpolation approximation are constructed,respectively.Then the existence and uniqueness of numerical solutions are discussed and analyzed.Finally,numerical simulations are used to compare the calculation errors of the ridge basis meshless method and the finite difference method in various situations.The numerical results show that the meshless method with ridge basis functions is feasible and effective for solving the time fractional two-flow domain model.