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Author: Rajesh Bhaskaran, Cornell University

1. Introduction
2. Finite Volume Method
3. Discretization
4. Algebraic Equations
5. Linearization
6. Algorithm

4. Algebraic Equations

Deriving System of Algebraic Equations

Example: Deriving System of Algebraic Equations

 

Check Your Understanding

Consider the algebraic equation for mass conservation at the end of the above video. This equation is of the form: Au1+Bu2+Cv1+Dv3=E where A,B,C,D,E are constant coefficients. From the explanation in the video, one can deduce that A=B=Δy/2. Denote the width of each cell in the x direction as Δx.

What is the value of C, the coefficient that multiples v1?  Answer: -Δx/2

Check Your Understanding

What is the value of the coefficient E in the equation in the previous question? Assume that that the inlet velocity is 1m/s in the x direction. Answer: Δy

Conservation is Built into FVM

 

Discretization: Overview

 


5. Linearization

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