761 research outputs found
Overture - Object-oriented tools for overset grid applications
The Overture framework is an object-oriented environment for solving partial differential equations in two and three space dimensions. It is a collection of C++ libraries that enables the use of finite difference and finite volume methods at a level that hides the details of the associated data structures. Overture can be used to solve problems in complicated, moving geometries using the method of overlapping grids. It has support for grid generation, difference operators, boundary conditions, data-base access and graphics. Short sample code segments are presented to show the power of this approach
On the smallest scale for the incompressible Navier-Stokes equations
It is proven that for solutions to the two- and three-dimensional incompressible Navier-Stokes equations the minimum scale is inversely proportional to the square root of the Reynolds number based on the kinematic viscosity and the maximum of the velocity gradients. The bounds on the velocity gradients can be obtained for two-dimensional flows, but have to be assumed to be three-dimensional. Numerical results in two dimensions are given which illustrate and substantiate the features of the proof. Implications of the minimum scale result to the decay rate of the energy spectrum are discussed
Numerical shock propagation using geometrical shock dynamics
A simple numerical scheme for the calculation of the motion of shock waves in gases based on Whitham's theory of geometrical shock dynamics is developed. This scheme is used to study the propagation of shock waves along walls and in channels and the self-focusing of initially curved shockfronts. The numerical results are compared with exact and numerical solutions of the geometrical-shock-dynamics equations and with recent experimental investigations
Computer and internet interventions to optimize listening and learning for people with hearing loss: accessibility, use, and adherence
Purpose: The aim of this research forum article was to examine accessibility, use, and adherence to computerized and online interventions for people with hearing loss. Method: Four intervention studies of people with hearing loss were examined: 2 auditory training studies, 1 working memory training study, and 1 study of multimedia educational support.
Results: A small proportion (approximately 15%) of participants had never used a computer, which may be a barrier to the accessibility of computer and Internet based interventions. Computer competence was not a factor in intervention use or adherence. Computer skills and Internet access influenced participant preference for the delivery method of the multimedia educational support program.
Conclusions: It is important to be aware of current barriers to computer and Internet-delivered interventions for people with hearing loss. However, there is a clear need to develop and future-proof hearing-related applications for online delivery
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A High-Order Accurate Parallel Solver for Maxwell's Equations on Overlapping Grids
A scheme for the solution of the time dependent Maxwell's equations on composite overlapping grids is described. The method uses high-order accurate approximations in space and time for Maxwell's equations written as a second-order vector wave equation. High-order accurate symmetric difference approximations to the generalized Laplace operator are constructed for curvilinear component grids. The modified equation approach is used to develop high-order accurate approximations that only use three time levels and have the same time-stepping restriction as the second-order scheme. Discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed. The implementation is optimized for component grids that are Cartesian, resulting in a fast and efficient method. The solver runs on parallel machines with each component grid distributed across one or more processors. Numerical results in two- and three-dimensions are presented for the fourth-order accurate version of the method. These results demonstrate the accuracy and efficiency of the approach
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Moving Overlapping Grids with Adaptive Mesh Refinement for High-Speed Reactive and Non-reactive Flow
We consider the solution of the reactive and non-reactive Euler equations on two-dimensional domains that evolve in time. The domains are discretized using moving overlapping grids. In a typical grid construction, boundary-fitted grids are used to represent moving boundaries, and these grids overlap with stationary background Cartesian grids. Block-structured adaptive mesh refinement (AMR) is used to resolve fine-scale features in the flow such as shocks and detonations. Refinement grids are added to base-level grids according to an estimate of the error, and these refinement grids move with their corresponding base-level grids. The numerical approximation of the governing equations takes place in the parameter space of each component grid which is defined by a mapping from (fixed) parameter space to (moving) physical space. The mapped equations are solved numerically using a second-order extension of Godunov's method. The stiff source term in the reactive case is handled using a Runge-Kutta error-control scheme. We consider cases when the boundaries move according to a prescribed function of time and when the boundaries of embedded bodies move according to the surface stress exerted by the fluid. In the latter case, the Newton-Euler equations describe the motion of the center of mass of the each body and the rotation about it, and these equations are integrated numerically using a second-order predictor-corrector scheme. Numerical boundary conditions at slip walls are described, and numerical results are presented for both reactive and non-reactive flows in order to demonstrate the use and accuracy of the numerical approach
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Parallel Computation of Three-Dimensional Flows using Overlapping Grids with Adaptive Mesh Refinement
This paper describes an approach for the numerical solution of time-dependent partial differential equations in complex three-dimensional domains. The domains are represented by overlapping structured grids, and block-structured adaptive mesh refinement (AMR) is employed to locally increase the grid resolution. In addition, the numerical method is implemented on parallel distributed-memory computers using a domain-decomposition approach. The implementation is flexible so that each base grid within the overlapping grid structure and its associated refinement grids can be independently partitioned over a chosen set of processors. A modified bin-packing algorithm is used to specify the partition for each grid so that the computational work is evenly distributed amongst the processors. All components of the AMR algorithm such as error estimation, regridding, and interpolation are performed in parallel. The parallel time-stepping algorithm is illustrated for initial-boundary-value problems involving a linear advection-diffusion equation and the (nonlinear) reactive Euler equations. Numerical results are presented for both equations to demonstrate the accuracy and correctness of the parallel approach. Exact solutions of the advection-diffusion equation are constructed, and these are used to check the corresponding numerical solutions for a variety of tests involving different overlapping grids, different numbers of refinement levels and refinement ratios, and different numbers of processors. The problem of planar shock diffraction by a sphere is considered as an illustration of the numerical approach for the Euler equations, and a problem involving the initiation of a detonation from a hot spot in a T-shaped pipe is considered to demonstrate the numerical approach for the reactive case. For both problems, the solutions are shown to be well resolved on the finest grid. The parallel performance of the approach is examined in detail for the shock diffraction problem
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