Inserting curved boundary layers for viscous flow simulation with high-order tetrahedra

We propose an a posteriori approach for generating curved meshes for viscous flow simulations composed by high-order tetrahedra. The proposed approach is performed in the following three steps: (1) generate a linear tetrahedral mesh for inviscid flow; (2) insert a boundary layer mesh, composed by linear tetrahedra, on the viscous part; and (3) convert the linear tetrahedral mesh to a curved and high-order mesh for viscous flow. This approach provides high-order tetrahedral meshes with boundary layer parts that are composed by elements that are: curved, valid, and of any interpolation degree. The main application of the obtained meshes is the simulation of viscous flow with high-order unstructured solvers. Since the obtained meshes are conformal and fully composed by tetrahedra, they can be used with any continuous and discontinuous Galerkin solver that features linear and high-order tetrahedra. That is, it does not require a solver for non-conformal and hybrid meshes. To show the applicability of the method, we present the flow around a curved geometry obtained with the hybridized discontinuous Galerkin method.