讲座主题：High-order positivity-preserving finite volume method for radiation diffusion problem on curvilinear grids

专家姓名：单丽

工作单位：汕头大学

讲座时间：2026年10月27日 08:30-09:30

讲座地点：腾讯会议：859-883-680

主办单位：烟台大学数学与信息科学学院

内容摘要：

In practice, the physical boundaries of radiation diffusion problems often involve complex curved boundaries, the use of polygonal grids to approximate the domain introduces grid induced errors that can limit the accuracy of numerical methods. Furthermore, most of existing positivity-preserving finite volume methods for these problems are generally restricted to second-order accuracy. In this paper, we propose a third-order positivity-preserving finite volume method for radiation diffusion problems on curvilinear grids. By applying a coordinate transformation, we reformulate the original problem as an equivalent anisotropic diffusion problem. To achieve high-order accuracy, our method only requires the reconstruction of the third-order remainder terms that arise during the construction of the numerical scheme, but not need to handle the additional terms arising from the coordinate transformation. In addition, we theoretically establish the third-order convergence of the proposed method. Several numerical examples are presented to verify the theoretical properties.

主讲人介绍：

单丽，汕头大学数学与计算机学院，副教授，毕业于西安交通大学计算数学专业，研究方向是偏微分方程数值解，主要研究方向是偏微分方程数值解，研究领域是复杂区域耦合流动模型的有限元方法构造与分析、辐射扩散问题的高阶有限体积方法。主持完成国家自然科学青年基金1项，天元项目2项，省级科研项目5项。 在 SIAM J.Numer.Anal.，J.Comput.Phys.，J.Sci.Comput.，中国科学：数学等期刊发表学术论文 30 余篇。现担任广东省工业与应用数学会常务理事，广东计算数学学会常务理事，中国工业与应用数学大数据专委会委员。