http://aero-comlab.stanford.edu/Papers/taiwan99.pdf

A perspective on computational algorithms for aerodynamic analysis and design

Algebraic grid generation

Nomenclature e = internal energy e = e{ + ¥211-u e^ = specific internal energy / =force F, G, H = vector fluxes J = Jacobian of coordinate transformation k = molecular heat conductivity n — outward normal P = pressure Pr = Prandtl number Prt = turbulent Prandtl number q =heat exchange Q = heat release t = time T = temperature u, v, w = velocity components in Cartesian frame x, y, z = Cartesian coordinates 7 = ratio of specific heats e = eddy viscosity coefficient X = bulk viscosity coefficient fji = molecular viscosity coefficient £, 17, f = transformed coordinates p = density T = stress tensor

An Assessment of Numerical Solutions of the Compressible Navier-Stokes Equations

Topography-dependent eikonal equation and its solver for calculating first-arrival traveltimes with an irregular surface

An assessment of numerical solutions of the compressible Navier-Stokes equations

One of the major approaches to numerical grid generation is the explicit algebraic expression of a physical grid as a function of a uniform grid in a rectangular computational coordinate system. The algebraic methods are based on mathematical interpolation, and the primary advantages are speed and directness. The relation between interpolation and grid generation is described. For three-dimensional grid generation, transfinite interpolation using the coordinate control processes developed in the multisurface method and two-boundary technique are advocated. Grid singularities encountered in three dimensions are discussed, and the exploration of multiple overlapping grids is proposed. Some aspects of interactive algebraic grid computation in three dimensions are discussed.

Three-dimensional algebraic grid generation

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Three-dimensional algebraic grid generation