A stable FSI algorithm for light rigid bodies in compressible flow

In this article we describe a stable partitioned algorithm that overcomes the added mass instability arising in fluid-structure interactions of light rigid bodies and inviscid compressible flow. The new algorithm is stable even for bodies with zero mass and zero moments of inertia. The approach is based on a local characteristic projection of the force on the rigid body and is a natural extension of the recently developed algorithm for coupling compressible flow and deformable bodies. Normal mode analysis is used to prove the stability of the approximation for a one-dimensional model problem and numerical computations confirm these results. In multiple space dimensions the approach naturally reveals the form of the added mass tensors in the equations governing the motion of the rigid body. These tensors, which depend on certain surface integrals of the fluid impedance, couple the translational and angular velocities of the body. Numerical results in two space dimensions, based on the use of moving overlapping grids and adaptive mesh refinement, demonstrate the behavior and efficacy of the new scheme. These results include the simulation of the difficult problem of a shock impacting an ellipse of zero mass.Comment: 32 pages, 20 figure

Variable high-order multiblock overlapping grid methods for mixed steady and unsteady multiscale viscous flows, part II: hypersonic nonequilibrium flows

The variable high-order multiblock overlapping (overset) grids method of Sjogreen & Yee (CiCP, Vol.5, 2008) for a perfect gas has been extended to nonequilibrium flows. This work makes use of the recently developed high-order well-balanced shock-capturing schemes and their filter counterparts (Wang et al., J. Comput. Phys., 2009, 2010) that exactly preserve certain non-trivial steady state solutions of the chemical nonequilibrium governing equations. Multiscale turbulence with strong shocks and flows containing both steady and unsteady components is best treated by mixing of numerical methods and switching on the appropriate scheme in the appropriate subdomains of the flow fields, even under the multiblock grid or adaptive grid refinement framework. While low dissipative sixth- or higher-order shock-capturing filter methods are appropriate for unsteady turbulence with shocklets, second- and third-order shock-capturing methods are more effective for strong steady or nearly steady shocks in terms of convergence. It is anticipated that our variable high-order overset grid framework capability with its highly modular design will allow an optimum synthesis of these new algorithms in such a way that the most appropriate spatial discretizations can be tailored for each particular region of the flow. In this paper some of the latest developments in single block high-order filter schemes for chemical nonequilibrium flows are applied to overset grid geometries. The numerical approach is validated on a number of test cases characterized by hypersonic conditions with strong shocks, including the reentry flow surrounding a 3D Apollo-like NASA Crew Exploration Vehicle that might contain mixed steady and unsteady components, depending on the flow conditions

Variable high-order multiblock overlapping grid methods for mixed steady and unsteady multiscale viscous flows, part II: hypersonic nonequilibrium flows

Abstract not provide

Computational issues and algorithm assessment for shock/turbulence interaction problems

The paper provides an overview of the challenges involved in the computation of flows with interactions between turbulence, strong shockwaves, and sharp density interfaces. The prediction and physics of such flows is the focus of an ongoing project in the Scientific Discovery through Advanced Computing (SciDAC) program. While the project is fundamental in nature, there are many important potential applications of scientific and engineering interest ranging from inertial confinement fusion to exploding supernovae. The essential challenges will be discussed, and some representative numerical results that highlight these challenges will be shown. In addition, the overall approach taken in this project will be outlined

An Improved High Order Finite Difference Method for Non-conforming Grid Interfaces for the Wave Equation

This paper presents an extension of a recently developed high order finite difference method for the wave equation on a grid with non-conforming interfaces. The stability proof of the existing methods relies on the interpolation operators being norm-contracting, which is satisfied by the second and fourth order operators, but not by the sixth order operator. We construct new penalty terms to impose interface conditions such that the stability proof does not require the norm-contracting condition. As a consequence, the sixth order accurate scheme is also provably stable. Numerical experiments demonstrate the improved stability and accuracy property

Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations

Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not perfect and there remain some issues. Concerning robustness, DG has undergone an extensive transformation over the past seven years into its modern form that provides statements on solution boundedness for linear and nonlinear problems. This chapter takes a constructive approach to introduce a modern incarnation of the DG spectral element method for the compressible Navier-Stokes equations in a three-dimensional curvilinear context. The groundwork of the numerical scheme comes from classic principles of spectral methods including polynomial approximations and Gauss-type quadratures. We identify aliasing as one underlying cause of the robustness issues for classical DG spectral methods. Removing said aliasing errors requires a particular differentiation matrix and careful discretization of the advective flux terms in the governing equations.Comment: 85 pages, 2 figures, book chapte

Psychiatric and cognitive phenotype in children and adolescents with myotonic dystrophy

Myotonic dystrophy type 1 (DM1) is the most frequent inherited neuromuscular disorder. The juvenile form has been associated with cognitive and psychiatric dysfunction, but the phenotype remains unclear. We reviewed the literature to examine the psychiatric phenotype of juvenile DM1 and performed an admixture analysis of the IQ distribution of our own patients, as we hypothesised a bimodal distribution. Two-thirds of the patients had at least one DSM-IV diagnosis, mainly attention deficit/ hyperactivity disorder and anxiety disorder. Two-thirds had learning disabilities comorbid with mental retardation on one hand, but also attention deficit, low cognitive speed and visual spatial impairment on the other. IQ showed a bi-modal distribution and was associated with parental transmission. The psychiatric phenotype in juvenile DM1 is complex. We distinguished two different phenotypic subtypes: one group characterised by mental retardation, severe developmental delay and maternal transmission; and another group characterised by borderline full scale IQ, subnormal development and paternal transmission

Designing Adaptive Low Dissipative High Order Schemes for Long-time Integrations

Classical stability and convergence theory are based on linear and local linearized analysis as the time steps and grid spacings approach zero. This theory offers no guarantee for nonlinear stability and convergence to the correct solution of the nonlinear governing equations. The use of numerical dissipation has been the key mechanism in combating numerical instabilities. Aside from acting as a post-processor step, most filters serve as some form of numerical dissipation. Without loss of generality, “numerical-dissipation/filter ” is, hereafter, referred to as “numerical dissipation”. Proper control of the numerical dissipation to accurately resolve all relevant multiscales of complex flow problems while still maintaining nonlinear stability and efficiency for long-time numerical integrations poses a great challenge to the design of numerical methods. The required type and amount of numerical dissipation are not only physical problem dependent, but also vary from one flow region to another. This is particularly true for unsteady high-speed shock/shear/boundary-layer/turbulence/acoustics interactions and/or combustion problems since the dynamics of the nonlinear effect of these flows are not well-understood, while longtime integrations of these flows have already stretched the limit of the current available supercomputers and the existing numerical methods. It is of paramount importance to have proper control on the type and amount of numerical dissipation in regions where it is needed but nowhere else. Inappropriate typ