4. Visualization Techniques
Society for Industrial and Applied Mathematics eBooks · 1998
The evaluation of computed data is an essential aspect of numerical flow simulation. To handle the vast amounts of data generated in the course of a computation, one can use some simple visualization techniques that are described in Section 4.1. Beyond these, we introduce further visualization techniques that have been developed specifically for flow applications in Sections 4.2 and 4.3. 4.1 Standard Techniques 4.1.1 Real-Valued Functions To obtain an image of a real-valued function defined on a two-dimensional domain , ƒ : Ω→ℝ , (x,y)↦ƒ (x,y) , such as the pressure p or temperature T (to be introduced later), the graph of the function Gƒ ≔{(x,y,z) ∈ Ω×ℝ∣z=ƒ (x,y)} ⊂ ℝ3 is often used. In this case it describes a two-dimensional surface over Ω obtained by lifting each point (x, y) ∈ Ω to its function value ƒ(x, y) (see Figure 4.1, left). Similarly, the level sets belonging to c ∈ ℝ, Nƒ (c) ≔{(x,y) ∈ Ω∣ƒ (x,y)=c} ⊂ R2 , consisting of all points (x, y) ∈ Ω at which the function ƒ takes the value c, can be used as well.