7,874 research outputs found
Status of research at the Institute for Computer Applications in Science and Engineering (ICASE)
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science is summarized
A new solution-adaptive grid generation method for transonic airfoil flow calculations
The clustering algorithm is controlled by a second-order, ordinary differential equation which uses the airfoil surface density gradient as a forcing function. The solution to this differential equation produces a surface grid distribution which is automatically clustered in regions with large gradients. The interior grid points are established from this surface distribution by using an interpolation scheme which is fast and retains the desirable properties of the original grid generated from the standard elliptic equation approach
Adaptive Mesh Refinement for Coupled Elliptic-Hyperbolic Systems
We present a modification to the Berger and Oliger adaptive mesh refinement
algorithm designed to solve systems of coupled, non-linear, hyperbolic and
elliptic partial differential equations. Such systems typically arise during
constrained evolution of the field equations of general relativity. The novel
aspect of this algorithm is a technique of "extrapolation and delayed solution"
used to deal with the non-local nature of the solution of the elliptic
equations, driven by dynamical sources, within the usual Berger and Oliger
time-stepping framework. We show empirical results demonstrating the
effectiveness of this technique in axisymmetric gravitational collapse
simulations. We also describe several other details of the code, including
truncation error estimation using a self-shadow hierarchy, and the
refinement-boundary interpolation operators that are used to help suppress
spurious high-frequency solution components ("noise").Comment: 31 pages, 15 figures; replaced with published versio
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