This study introduces a novel parallel algorithm for efficiently solving two-dimensional advection-diffusion problems with constant diffusion coefficient, specifically designed for implementation on GPU. The algorithm is compact, conservative, and inherently parallel, offering second-order accuracy in time and fourth-order accuracy in space. It employs a second-order operator splitting method to decompose the two-dimensional problem into one-dimensional subproblems, significantly enhancing parallelism in computations. The convective term is addressed using the characteristic method, which ensures high accuracy in time and allows for larger time steps. The conservative interpolation technique is implemented for integration within the Lagrangian tracking cell. For the diffusion term, we average along the characteristic curves and derive the discrete fluxes that are continuous at the cell boundaries. Taking advantage of the compact scheme, only three cells are required for the unknowns to achieve spatial fourth order accuracy. The primary computational tasks are performed on the GPU, distributing the computational load evenly across multiple cores. Numerical experiments demonstrate the conservation property and convergence rates of the new algorithm and its effectiveness in solving problems with steep fronts. The results also indicate the algorithm’s superior computational speed compared to traditional CPU computations.

付凯, 中国海洋大学数学科学学院副教授、博士生导师。2012年于山东大学获得计算数学博士学位, 2013年至2015年在加拿大约克大学担任博士后研究员。研究方向为偏微分方程数值解和环境数值模拟, 在对流扩散问题计算方法和环境模型数值计算领域取得了重要研究成果。在SIAM Journal on Scientific Computing, Journal of Computational Physics, Journal of Scientific Computing, Computer Physics Communications, Atmospheric Environment, Atmospheric Research等国际知名学术期刊上发表论文20余篇。主持国家自然科学基金青年科学基金项目、面上项目, 以及山东省优秀中青年科学家科研奖励基金、山东省自然科学基金面上项目等多项科研项目。