Space-Time Mapping Analysis for the Accurate Calculation of Complex Unsteady Flows*

In this work, a new methodology for computing unsteady flow problems is presented. This method treats the temporal direction identically to the spatial directions, transforming a 2- or 3- dimensional time-marching problem to a 3- or 4-dimensional iterative problem. This transformation allows much greater flexibility in grid generation and solution procedure, and is uniquely suited to the distributedmemory parallel-processing computers that are widely available.

[1]  Isaac Fried,et al.  Finite-element analysis of time-dependent phenomena. , 1969 .

[2]  Michael A. Jensen,et al.  A massively parallel computation strategy for FDTD: time and space parallelism applied to electromagnetics problems , 1995 .

[3]  R. R. Mankbadi,et al.  Evaluation of Boundary Conditions for the Gust-Cascade Problem , 1998 .

[4]  Analysis of mixed and stabilized space-time finite element methods for the Navier-Stokes equations , 2001 .

[5]  Richard Benney,et al.  COMPUTATIONAL AERODYNAMICS OF A PARATROOPER SEPARATING FROM AN AIRCRAFT , 2001 .

[6]  M. Carpenter,et al.  Several new numerical methods for compressible shear-layer simulations , 1994 .

[7]  Sin-Chung Chang The Method of Space-Time Conservation Element and Solution Element-A New Approach for Solving the Navier-Stokes and Euler Equations , 1995 .

[8]  Herman Deconinck,et al.  Space-time residual distribution schemes for hyperbolic conservation laws , 2001 .

[9]  Michael B. Giles,et al.  Nonreflecting boundary conditions for Euler equation calculations , 1990 .

[10]  Christopher K. W. Tam,et al.  Numerical Simulation of the Generation of Axisymmetric Mode Jet Screech Tones , 1998 .

[11]  G. Raithby,et al.  An Integrated Space-Time Finite Volume Method for Moving Boundary Problems , 1998 .

[12]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics. X - The compressible Euler and Navier-Stokes equations , 1991 .

[13]  A. Jameson,et al.  Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes , 1981 .

[14]  Hafiz M. Atassi,et al.  Numerical solutions of the linearized Euler equations for unsteady vortical flows around lifting airfoils , 1990 .

[15]  C. Tam,et al.  Dispersion-relation-preserving finite difference schemes for computational acoustics , 1993 .

[16]  Marek Behr,et al.  The Shear-Slip Mesh Update Method , 1999 .

[17]  Hafiz M. Atassi,et al.  A finite difference, frequency-domain numerical scheme for the solution of the gust response problem , 1995 .

[18]  André Garon,et al.  Unstructured tetrahedral mesh adaptation for two-dimensional space-time finite elements , 2000 .

[19]  Ray Hixon,et al.  Validation of a High-Order Prefactored Compact Code on Nonlinear Flows with Complex Geometries , 2001 .

[20]  M. Nallasamy,et al.  Effect of Grid Singularities on the Solution Accuracy of a CAA Code , 2003 .