수치해석 c프로그래밍

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수치해석 c프로그래밍

목차

1. Problem
2. Idea
3. Programming with C
4. Result
5. Discussion
6. Reference

본문내용

1. Problem
Write C or FORTRAN to solve the following problem.
For turbulent flow of fluids in an interconnected network (see Figure below), the flow rate V from one node to another is about proportional to the square root of the difference in pressures at the nodes. (Thus fluid flow differs from flow of electrical current in a network in that nonlinear equations result.) For the conduits in Figure, find the pressure at each node. The values of b represent conductance factors in the relation vij=bij(pi-pj)1/2.
These equations can be set up for the pressures at each node:

At Node 1: 0.3(500-p1)1/2=0.2(p1-p2)1/2+0.1(p1-p3)1/2
Node 2: 0.2(p1-p2)1/2=0.1(p2-p4)1/2+0.2(p2-p3)1/2
Node 3: 0.1(p1-p3)1/2+0.2(p2-p3)1/2=0.1(p3-p4)1/2
Node 4: 0.1(p2-p4)1/2+0.1(p3-p4)1/2=0.2(p4-0)1/2

2. Idea
Gauss-seidel method를 적용시키기 위해, 주어진 4개식의 좌변 우변을 각각 제곱해서 p1, p2, p3, p4에 대한 식으로 정리하면 아래와 같다.

p1=(1/0.14)(45+0.04p2+0.01p3-0.04(p1-p2)1/2(p1-p3)1/2)
p2=(1/0.09)(0.04p1+0.04p3+0.01p4-0.04(p2-p4)1/2(p2-p3)1/2)
p3=(1/0.06)(0.01p1+0.04p2+0.01p4+0.04(p1-p3)1/2(p2-p3)1/2)
p4=(1/0.06)(0.01p2+0.01p3+0.02(p2-p4)1/2(p3-p4)1/2)

참고 자료

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