Introduction to Computational Fluid Dynamics
For advanced undergraduate and first year graduate students in mechanical, aerospace and chemical engineering, this textbook emphasizes understanding CFD through physical principles and examples.
TABLE OF CONTENTS Introduction to Computational Fluid Dynamics
Chapter 8: Numerical Grid Generation
8.1 Introduction
As mentioned in Chapter 6, curvilinear grid generation for 2D domains involves specification of functions
| (8.1) |  |
where ? 1, ? 2 are curvilinear coordinates and x 1, x 2 are Cartesian coordinates. These two functions can be generated in two ways: (1) by algebraic specification or (2) by differential specification.
Algebraic specification is typically employed in 1D problems but can also be employed in 2D problems when the domain is simple (Section 8.2). For complex domains, however, differential grid generation is preferred. In this type, functions (8.1) are generated by solving differential equations with dependent variables x 1 and x 2. The differential equations can be of parabolic, hyperbolic, or elliptic type [81]. However, we shall consider the most commonly used elliptic grid generation technique (Sections 8.3 and 8.4)
The unstructured meshes again can be generated in a variety of ways. Two types will be considered: (1) generation by exploiting structuredness and (2) automatic mesh generation (Section 8.5).
8.2 Algebraic Grid Generation
8.2.1 1D Domains
The objective of grid generation is to locate nodes such that they are closely spaced in regions where the dependent variable ? in the transport equations is expected to have steep gradients and sparsely spaced in regions where the gradients are small. This ensures that accurate solutions are economically obtained.
Consider a 1D domain of length L with N nodes so that there are N ?2 control volumes. One may now specify either...
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