Anisotropic mesh adaptation for high-Order meshes in two dimensions

Error estimation and mesh adaptation are essential for accurate and efficient computational fluid dynamics simulations, but traditional approaches for high-order curved meshes face significant robustness issues. Traditionally, curved meshes are first made linear and then adapted and re-curved at the end of the adaptation process. Making the mesh linear and re-curving the mesh risks creating negative Jacobians for anisotropic elements, which adversely affects the robustness of the mesh adaptation process. We developed a novel method for performing anisotropic mesh adaptation on high-order curved meshes. This process extends existing edge primitive operations for mesh adaptation to high-order meshes. In contrast to the traditional procedure, our method keeps the mesh valid and curved during the entire adaptation process, leading to more robust mesh adaptation. The method extends traditional linear mesh modification operators to arbitrary-order curved meshes. Results for four test cases demonstrate that this method produces valid curved meshes with various aspect ratios. The test cases show that our method recovers optimal high-order error convergence rates and performs similarly to existing global remeshing strategies. This appraoch enables reliable automated of mesh adaptation which is necessary to realize the benefits of high-order computational fluid dynamics methods.