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We develop new high‐order positive, monotone and convex interpolations, which are to be used in the multigrid context. This means that the value of the interpolant is calculated only at the midpoints lying between the locations of the given values. As a consequence, these interpolants can be calculated very efficiently. They are then tested in a time‐dependent very large scale integration process simulation application.

The numerical solution of the diffusion equation in VLSI process simulation leads to large systems of nonlinear equations which have to be solved at every time step. For this purpose, a multigrid (MG) algorithm with locally refined grids is constructed. It is demonstrated that the method used here yields typical MG algorithm convergence rates, and reduces the amount of work considerably. The local refinements are controlled by an estimation of the discretization error which is calculated within the nonlinear MG method (FAS) and requires no extra computational work.

An optimized multigrid method (NSFLEX‐MG) for the NSFLEX‐code (Navier‐Stokes solver using characteristic flux extrapolation) of MBB (Messerschmitt Bolkow Blohm GmbH) is described. The method is based on a correction scheme and implicit relaxation procedures and is applied to two‐dimensional test cases. The principal feature of the flow solver is a Godunov‐type averaging procedure based on the eigenvalues analysis of the Euler equations by means of which the inviscid fluxes are evaluated at the finite volume faces. Viscous fluxes are centrally differenced at each cell face. The performance of NSFLEX‐MG is demonstrated for a large range of Mach numbers for compressible inviscid and viscous (laminar and turbulent) flows over a RAE‐2822 airfoil and over a NACA‐0012 airfoil.

The purpose of this study is to model the dynamic characteristics of an opened supersonic disk-gap-band parachute.

A fluid-structure interaction (FSI) method with body-fitted mesh is used to simulate the supersonic parachute. The compressible flow is modeled using large-eddy simulation (LES). A contact algorithm based on the penalty function with a virtual contact domain is proposed to solve the negative volume problem of the body-fitted mesh. Automatic unstructured mesh generation and automatic mesh moving schemes are used to handle complex deformations of the canopy.

The opened disk-gap-band parachute is simulated using Mach 2.0, and the simulation results fit well with the wind tunnel test data. It is found that the LES model can successfully predict large-scale turbulent vortex in the flow. This study also demonstrates the capability of the present FSI method as a tool to predict shock oscillation and breathing phenomenon of the canopy.

The contact algorithm based on the penalty function with a virtual contact domain is proposed for the first time. This methodology can be used to solve the negative volume problem of the dynamic mesh in the flow field.