A new Lagrangian-Eulerian shell-fluid coupling algorithm based on level sets

We propose a computational method for the coupled simulation of a compressible flow interacting with a thin-shell structure undergoing large deformations. An Eulerian finite volume formulation is adopted for the fluid and a Lagrangian formulation based on subdivision finite elements is adopted for the shell response. The coupling between the fluid and the solid response is achieved via a novel approach based on level sets. The basic approach furnishes a general algorithm for coupling Lagrangian shell solvers with Cartesian grid based Eulerian fluid solvers. The efficiency and robustness of the proposed approach is demonstrated with a airbag deployment simulation. It bears emphasis that in the proposed approach the solid and the fluid components as well as their coupled interaction are considered in full detail and modeled with an equivalent level of fidelity without any oversimplifying assumptions or bias towards a particular physical aspect of the problem.

Viscous layer meshes from level sets on cartesian meshes

The long term goal of our work is to enable rapid prototyping design optimization to take place on geometries of arbitrary size in a spirit of a real time computer game. In recent papers we have reported the integration of a Level Set based geometry kernel with an octree-based cut-Cartesian mesh generator, RANS flow solver and post-processing all within a single piece of software - and all implemented in parallel with commodity PC clusters as the target. This work has shown that it is possible to eliminate all serial bottlenecks from the CED Process. This paper reports further progress towards our goal; in particular we report on the generation of viscous layer meshes to bridge the body to the flow across the cut-cells. The Level Set formulation, which underpins the geometry representation, is used as a natural mechanism to allow rapid construction of conformal layer meshes. The guiding principle is to construct the mesh which most closely approximates the body but remains solvable. This apparently novel approach is described and examples given.

Using Level Sets as the basis for a scalable, parallel geometry engine and mesh generation system

The background to this review paper is research we have performed over recent years aimed at developing a simulation system capable of handling large scale, real world applications implemented in an end-to-end parallel, scalable manner. The particular focus of this paper is the use of a Level Set solid modeling geometry kernel within this parallel framework to enable automated design optimization without topological restrictions and on geometries of arbitrary complexity. Also described is another interesting application of Level Sets: their use in guiding the export of a body-conformal mesh from our basic cut-Cartesian background octree - mesh - this permits third party flow solvers to be deployed. As a practical demonstrations meshes of guaranteed quality are generated and flow-solved for a B747 in full landing configuration and an automated optimization is performed on a cooled turbine tip geometry. Copyright © 2009 by W.N.Dawes.

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.