The Application Of The Time Domain Radial Integral Boundary Element Method In 2D One-Phase Solidification

Boundary element method(BEM)has been widely used in engineering and scientific computing due to its advantages,and has become one of the most important numerical methods.Compared with other numerical methods,BEM has some unique merits including dimensionality reduction and only boundary discretization is required.However,for complex engineering problems it is difficult to obtain the basic solution,and this is the main reason that restricts the development of BEM.In practice,the basic solution of simple problems is used for transient problem,nonlinear problem and other complex problem,as a result,the domain integral terms still exist in the governing equation.So far,the radial integration method is recognized as one of the most effective and accurate methods for converting domain integral into boundary integral.In this paper,the one-phase solidification heat transfer problem is studied based on the radial integral boundary element method(RIBEM)..In this study,the RIBEM is coupled with the precise integration method(PIM)to form a new time-domain precise integration boundary element method(TDPIBEM)for the two-dimensional one-phase solidification heat conduction problem.Firstly,the domain integral equation of the transient heat transfer problem is given,where the basic solution of the steady heat conduction problem is used as weight function,and the discreted ordinary differential equation set of the problem is obtained.Next,PIM which is unconditional stable is used to the equations,and the temperature field as well as the heat flux in the phase change interface are obtained.Finally,the front-tracking method(FTM)is used to determine the position of the phase change interface.In this way,an effective numerical analysis method is proposed for one-phase solidification heat conduction problem.Numerical results with high precision can be obtained with different maximum solidification thicknesses(different time steps).Results also indicate that the proposed method has the advantages of high accuracy,insensitivity to time steps,fewer of iteration numbers,and high stability.This work has extended the application of RIBEM,and also provides a preliminary work of extending RIM to deal with complex phase changing problems and nonlinear problems.