Mesh Generation and ongoing Developments

This session presents ongoing development on mesh generation and other application of spectral/hp element within Nektar++ framework and comprises the following talks 1. Implementation of the Parareal Algorithm in the Nektar++ Spectral/hp Element Framework with Applications to Linear and Non-Linear Problems 2. NekMesh: High-Order Mesh Generation and Adaptation with NekMesh 3. Locomotion of microparticles close to wallImplementation of the Parareal Algorithm in the Nektar++ Spectral/hp Element Framework with Applications to Linear and Non-Linear ProblemsNektar++ is an open-source spectral-hp element framework designed to support the development of solvers for partial differential equations. The software supports various discretization techniques, notably both continuous and discontinuous Galerkin, in combination with both modal and nodal expansions. Recently, time-parallel integration techniques are recognized as a potential solution to further increase concurrency and speed-up beyond the limits of strong scaling obtained from a pure spatial domain decomposition. Amongst the various time-parallel approaches proposed in the literature, the Parareal algorithm has become one of the most popular one. Parareal is a non-intrusive, iterative-based approach, exploiting a fine and coarse solvers to achieve time-parallelism and can be applied to both linear and non-linear problems. The efficient implementation of the Parareal algorithm in the Nektar++ open-source framework is described in this work. Application to multiple linear and non-linear problems is shown.NekMesh: High-Order Mesh Generation and AdaptationFirst, we present the redesigned high-order mesh generation pipeline from third-party straight-sided meshes for very complex industrial geometries. This workflow integrates all NekMesh high-order mesh curving, surface and volume optimizations, boundary-layer splitting and untangling. We showcase the meshed complex geometries but also the recent advances in the workflow such as multiple sources of CAD-truth, the tools for assessing geometrical accuracy, mesh quality and ensuring periodicities. The main focus of this talk is the mesh modification techniques that extend the mesh generation capabilities but also allow a-posteriori mesh optimization and adaptation. We provide a brief overview of the novel h- and the existing r- and p-adaptation techniques in NekMesh and Nektar++ for both 2D and 3D problems. Then, we combine these in r-p, h-p and h-r-p adaptations, showing the advantages of applying all three adaptation techniques simultaneously for compressible flows.