This paper presents an efficient collocation method which combines the generalized finite difference method (GFDM) with the Krylov deferred correction (KDC) method for the long-time simulation of heat and mass transport on evolving surfaces. The KDC method utilizes a pseudo-spectral-type temporal collocation formulation to discretize the time-dependent surface heat and mass transport equation in each time marching step, where the time derivatives at the collocation points are introduced as the new unknown variables. A low-order time marching scheme is then applied as an effective preconditioner in the Jacobian-Free Newton-Krylov framework to decouple the spatial surface PDEs at different collocation nodes. Each decoupled surface PDE is then solved by the meshless GFDM, where both the continuous-form evolving surfaces defined by parametric equations and discretized-form evolving surfaces composed of point clouds are considered in the GFDM spatial discretization. Numerical experiments show that the combined GFDM-KDC solver is a promising numerical scheme for long-time evolution simulation of heat and mass transport on intractable evolving surfaces.

本文提出了一种将广义有限差分法 (GFDM) 与 Krylov 延迟校正 (KDC) 方法相结合的高效配置方法，用于长期模拟演化表面上的热质传输。KDC方法利用伪谱型时间配置公式对每个时间推进步骤中的时间相关表面热质传输方程进行离散化，其中将配置点处的时间导数作为新的未知变量引入。然后在 Jacobian-Free Newton-Krylov 框架中应用低阶时间推进方案作为有效的预处理器，以解耦不同配置节点处的空间表面 PDE。然后通过无网格 GFDM 求解每个解耦表面 PDE，在 GFDM 空间离散化中考虑了由参数方程定义的连续形式的演化表面和由点云组成的离散形式的演化表面。数值实验表明，组合的 GFDM-KDC 求解器是一种很有前途的数值方案，用于在难以处理的演化表面上进行热量和质量传输的长期演化模拟。