Discretization of Surfaces

Numerical solution of unsteady flow on airfoils with vibrating local flexible membrane

  Unsteady flow separation on the airfoils with local flexible membrane (LFM) has been investigated in transient and laminar flows by the finite volume element method. A unique feature of the present method compared with the common computational fluid dynamic softwares, especially ANSYS CFX, is the modification using the physical influence scheme in convection fluxes at cell surfaces. In contr...

Convergent discrete Laplace-Beltrami operators over surfaces

The convergence problem of the Laplace-Beltrami operators plays an essential role in the convergence analysis of the numerical simulations of some important geometric partial differential equations which involve the operator. In this note we present a new effective and convergent algorithm to compute discrete Laplace-Beltrami operators acting on functions over surfaces. We prove a convergence t...

Koiter's Thin Shells on Catmull-Clark Limit Surfaces

We present a discretization of Koiter’s model of elastic thin shells based on a finite element that employs limit surfaces of Catmull–Clark’s subdivision scheme. The discretization can directly be applied to control grids of Catmull–Clark subdivision surfaces, and, therefore, integrates modeling of Catmull–Clark subdivision surfaces with analysis and optimization of elastic thin shells. To test...

Discretization of Surfaces and Integrable Systems

Deformable Surfaces using Physically-Based Particle Systems

This paper presents a simple method for creating and animating deformable surfaces using physically-based modeling. We represent a deformable surface as particle systems. Simple methods, such as, analytical solutions of the motion equations, discretization and time-step method, are used to solve the simulation equations. So, the surfaces have better stability and much faster speed of calculatio...