This work aims to verify different numerical algorithms under different types of mesh. Our area of interest is the algorithms for the numerical solution of partial differential equations describing the incompressible fluid movement. The numerical resolution of these partial differential equations is sensitive to the mesh used, especially for fluid simulations with complex geometry. We will do the numerical simulations based on Laplace, Burgers and Navier-Stokes equations using the finite volume method. For the simulations of the Navier-Stokes equation we will use the OpenFoam-2.1 solvers based in SIMPLE and PISO algorithms. To calculate the error, we will build analytical solutions based on the method of manufactured solutions. We will study the order convergence for several numerical schemes using different types of mesh, structured and unstructured under different boundary conditions. We will study the impact of mesh perturbation on the convergence. Finally, we will do comparisons of convergence orders for the errors given by the manufactured solution and by the interpolation error.
We investigate the stability of a trailing vortex using mean flow profiles given by an approximate solution of the Navier-Stokes equations. The axial and tangential velocity profiles obtained from this solution, deduced by Moore & Saffman (1973), agree well with experiments involving wings at slight angles of attack. In particular, jet-like and wake-like flows near the center of the vortex provide a better description of the axial flow than the much-studied Batchelor vortex. We find that they accurately describe the flow at short and intermediate distances behind the wingtip. Growth rates for unstable perturbations will be presented and shown to be considerably larger than those for the Batchelor vortex.
Weakly electric fish use electrolocation - the detection of electric fields - to sense their environment. The task of electrolocation involves the decoding of the third dimension "depth" from a two-dimensional electric image. In this talk we present two advances in the area of depth-perception. First, we develop a model for electrolocation based on a single parameter, namely the width of the electric image. In contrast to previous suggested algorithms, our algorithm would only require a single narrow tuned topological map to accurately estimate distance. This model is used to study the effects of electromagnetic noise and the presence of stochastic resonance. Second, considering the problem of depth perception from the perspective of information constraints, we ask; how much information is necessary for location disambiguation? That is, what is the minimum amount of information that fish would need to localize an object? This inverse problem approach gives us insight into biological electrolocation and provides a guide for future experimental work.
SmartMesh is a generic tool to control unstructured triangular meshes. Using a Delaunay mesh generator, the geometric domain is discretized with unstructured triangles. This initial mesh is used to compute geometric domain characteristics such as boundary curvature, distance of a vertex to a boundary, distance between two boundaries, etc. These geometric characteristics are transformed into size tensors at each mesh vertex by functions specified by the user through an external file. Finally, an adapted mesh is create using the size tensors computed on the initial mesh. Examples are provided for inviscid, viscous and turbulent flows for internal and external geometries.
We present an immersed boundary (IB) method for solving fluid flow problems in presence of static and moving rigid objects. A finite element method is used starting from a base mesh which does not represent exactly rigid objects (non body-conforming mesh). At each time step, the base mesh is locally modified to provide a new mesh fitting the boundary of the rigid objects. The mesh is also locally improved using edge swapping to enhance the quality of the elements. The Navier-Stokes equations are then solved on this new mesh. The velocity of moving objects is imposed through standard Dirichlet boundary conditions. We consider a number of test problems and compare the numerical solutions with those obtained on classical body-fitted meshes whenever possible.