This paper deals with a simple and straightforward procedure for automatic generation of finiteelement or finite-volume meshes of spheroidal domains, consisting of tetrahedra. Besides the equation of the boundary, the generated meshes depend only on an integer parameter, whose value is associated with the degree of refinement. More specifically the procedure applies to the case where the bounda...

This paper discusses the dimensions of the spline spaces over T-meshes with lower degree. Two new concepts are proposed: extension of T-meshes and spline spaces with homogeneous boundary conditions. In the dimension analysis, the key strategy is linear space embedding with the operator of mixed partial derivative. The dimension of the original space equals the difference between the dimension o...

1 OVERVIEW This guide describes a collection of programs for (1) creating and reening tri-angulations on surfaces, and (2) solving integral equations using collocation methods over these triangulations. The main purpose of this package is to allow for experimentation with numerical methods for solving boundary integral equations that are deened on piecewise smooth surfaces in R 3. General surve...

The paper focuses on the development of a framework for high-order compact finite volume discretization of the threedimensional scalar advection–diffusion equation. In order to deal with irregular domains, a coordinate transformation is applied between a curvilinear, non-orthogonal grid in the physical space and the computational space. Advective fluxes are computed by the fifth-order upwind sc...

Abstract Airborne wind energy (AWE) is an emerging technology for the conversion of into electricity by flying crosswind patterns with a tethered aircraft. Having proper understanding unsteady interaction air highly dynamic system during operation key to developing viable AWE systems. High fidelity simulation tools are needed correctly predict these interactions, which will provide insights des...

An unconditionally stable thermal lattice Boltzmann method (USTLBM) is proposed in this paper for simulating incompressible thermal flows. In USTLBM, solutions to the macroscopic governing equations that are recovered from lattice Boltzmann equation (LBE) through Chapman–Enskog (C-E) expansion analysis are resolved in a predictor–corrector scheme and reconstructed within lattice Boltzmann frame...

This work introduces “generalized meshes”, a type of meshes suited for the discretization partial differential equations in non-regular geometries. Generalized extend regular simplicial by allowing overlapping elements and more flexible adjacency relations. They can have several distinct “generalized” vertices (or edges, faces) that occupy same geometric position. These generalized facets are n...

We present an immersed-boundary algorithm for incompressible flows with complex boundaries, suitable for Cartesian or curvilinear grid system. The key stages of any immersed-boundary technique are the interpolation of a velocity field given on a mesh onto a general boundary (a line in 2D, a surface in 3D), and the spreading of a force field from the immersed boundary to the neighboring mesh poi...

Given an unstructured mesh consisting of quadrilaterals and triangles (we allow both planar non-planar meshes arbitrary topology), we present the construction quadratic splines mixed smoothness — C1 smooth away from regions T C0 otherwise. The have several useful B-spline-like properties – partition unity, non-negativity, local support linear independence for straightforward imposition boundary...