In this paper, a meshless BEM based on the radial integration method is developed to solve transient non-homogeneous convection-diffusion problem with spatially variable velocity and time-dependent source term. The Green function served as the fundamental solution is adopted to derive the boundary domain integral equation about the normalized field quantity. The two-point backward finite difference technique is utilized to discretize the time-dependent terms in the integral equation, which results in that the final integral equation formulation is only related with the normalized field quantity at the current time and has three domain integrals. Both two domain integrals regarding the normalized field quantity at the current and previous times are transformed into boundary integrals by using radial integration method and radial basis function approximation. For domain integral about the source term being known function of time and coordinate, radial basis functions approximation is still adopted to make the transformed boundary integral be evaluated only once, not at each time level. A pure boundary element algorithm with boundary-only discretization and internal points is established and the system of equations is assembled like the corresponding steady problem. Four numerical examples are given to demonstrate the accuracy and effectiveness of the present method.

为了解决瞬态非均匀对流扩散问题，提出了一种基于径向积分法的无网格边界元方法。采用格林函数作为基本解，导出关于归一化场量的边界域积分方程。利用两点向后有限差分技术对积分方程中的时间相关项进行离散化，结果是最终的积分方程公式仅与当前时间的归一化场量有关，并且具有三个域积分。通过使用径向积分法和径向基函数逼近，将关于当前和先前时间的归一化场量的两个域积分都转换为边界积分。对于关于源项的域积分是时间和坐标的已知函数，仍然采用径向基函数逼近来使变换后的边界积分仅被评估一次，而不是在每个时间级别进行评估。建立了具有仅边界离散和内部点的纯边界元算法，并像相应的稳态问题一样组装了方程组。给出了四个数值例子来说明本方法的准确性和有效性。仍然采用径向基函数逼近，以使变换后的边界积分仅被评估一次，而不是在每个时间级别进行评估。建立了具有仅边界离散和内部点的纯边界元算法，并像相应的稳态问题一样组装了方程组。给出了四个数值例子来说明本方法的准确性和有效性。仍然采用径向基函数逼近，以使变换后的边界积分仅被评估一次，而不是在每个时间级别进行评估。建立了具有仅边界离散和内部点的纯边界元算法，并像相应的稳态问题一样组装了方程组。给出了四个数值例子来说明本方法的准确性和有效性。