Unstructured Triangular Elements Research Articles

Local mesh adaptation technique for front tracking problems

A numerical model is developed for the simulation of moving interfaces in viscous incompressible flows. The model is based on the finite element method with a pseudo-concentration technique to track the front. Since a Eulerian approach is chosen, the interface is advected by the flow through a fixed mesh. Therefore, material discontinuity across the interface cannot be described accurately. To remedy this problem, the model has been supplemented with a local mesh adaptation technique. This latter consists in updating the mesh at each time step to the interface position, such that element boundaries lie along the front. It has been implemented for unstructured triangular finite element meshes. The outcome of this technique is that it allows an accurate treatment of material discontinuity across the interface and, if necessary, a modelling of interface phenomena such as surface tension by using specific boundary elements. For illustration, two examples are computed and presented : the broken dam problem and the Rayleigh-Taylor instability

Topological refinement procedures for triangular finite element meshes

This paper presents a topological approach to improve the quality of unstructured triangular finite element meshes. Topological improvement procedures are presented both for elements that are interior to the mesh and for elements connected to the boundary. Optimal ordering of the topology improvement operations and their efficient implementation is also discussed. Several example meshes are included to demonstrate the effectiveness of the approach in improving element quality in a finite element mesh.

Shock-Wave/Boundary Layer Interactions at Hypersonic Speed by an Implicit Navier-Stokes Solver

Abstract An implicit Navier-Stokes solver has been used to calculate steady-state solutions for several typical hypersonic geometries. Particular attention was paid to the resulting complex interactions between the shock waves and the boundary layers. The numerical method was based on either an upwind Galerkin finite-volume approach or a symmetric TVD extension for the convective fluxes, with a centred Galerkin finite-element solution of the viscous fluxes. The computational grid consisted of structured finite elements within the boundary layer region and unstructured triangular elements elsewhere. Results are presented for the case of a compression ramp in two different flow situations. The first concerns a high Reynolds number flow while the second is at a higher Mach number bui a lower Reynolds number. Comparisons with experimental data are given. Subsequently computed results for two generic canopy flows over a double ellipse are also presented. These have been calculated for wind tunnel conditions at...