A penalty approach to the numerical simulation of a constrained wave motion

The main goal of this article is to investigate the numerical solution of a vector-valued nonlinear wave equation, the nonlinearity being of the Ginzburg-Landau type, namely (|u|2-1)u. This equation is obtained when treating by penalty a constrained wave-motion, where the displacement vector is of constant length (1 here, after rescaling). An important step of the approximation process is the construction of a time discretization scheme preserving-in some sense-the energy conservation property of the continuous model. The stability properties of the above scheme are discussed. The authors discuss also the finite element approximation and the quasi-Newton solution of the nonlinear elliptic system obtained at each time step from the time discretization. The results of numerical experiments are presented; they show that for the constraint of the original wave problem to be accurately verified we need to use a small value of the penalty parameter

Application of the penalty coupling method for the analysis of blood vessels

Due to the significant health and economic impact of blood vessel diseases on modern society, its analysis is becoming of increasing importance for the medical sciences. The complexity of the vascular system, its dynamics and material characteristics all make it an ideal candidate for analysis through fluid structure interaction (FSI) simulations. FSI is a relatively new approach in numerical analysis and enables the multi-physical analysis of problems, yielding a higher accuracy of results than could be possible when using a single physics code to analyse the same category of problems. This paper introduces the concepts behind the Arbitrary Lagrangian Eulerian (ALE) formulation using the penalty coupling method. It moves on to present a validation case and compares it to available simulation results from the literature using a different FSI method. Results were found to correspond well to the comparison case as well as basic theory

Shape optimization of Stokesian peristaltic pumps using boundary integral methods

This article presents a new boundary integral approach for finding optimal shapes of peristaltic pumps that transport a viscous fluid. Formulas for computing the shape derivatives of the standard cost functionals and constraints are derived. They involve evaluating physical variables (traction, pressure, etc.) on the boundary only. By emplyoing these formulas in conjuction with a boundary integral approach for solving forward and adjoint problems, we completely avoid the issue of volume remeshing when updating the pump shape as the optimization proceeds. This leads to significant cost savings and we demonstrate the performance on several numerical examples

Approaches and possible improvements in the area of multibody dynamics modeling

A wide ranging look is taken at issues involved in the dynamic modeling of complex, multibodied orbiting space systems. Capabilities and limitations of two major codes (DISCOS, TREETOPS) are assessed and possible extensions to the CONTOPS software are outlined. In addition, recommendations are made concerning the direction future development should take in order to achieve higher fidelity, more computationally efficient multibody software solutions