An algorithm for solving a generalized bernoulli equation

Date

6-1993

Degree

Bachelor of Science in Applied Mathematics

College

College of Arts and Sciences (CAS)

Adviser/Committee Chair

Rodolfo M. Castillo

Abstract

An explicit finite difference method had been widely used in solving a Bernoulli type equation with changing form of constitutive relations. The practical application is on simulating the pressure drop in the flow of water in a geothermal well. Though this numerical scheme is relatively easy to apply, the associated truncation errors and the rounding-off errors are relatively large, hence, unstable. This study outlines the development of a mixed implicit differencing-iterative refinement method for pressure drop simulation, along with a Newtonian iterative method for solving the resulting system of nonlinear equations at each refinement step. The method is validated against three family of equations with closed-form solutions. While this implicit formulation requires a dozen times more work than does the implicit one, it is shown to dramatically decrease the absolute errors and thus, to yield a more stable solution.

Language

English

Location

UPLB Main Library Special Collections Section (USCS)

Call Number

Thesis

Document Type

Thesis

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