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9-010-TravelingWave-ModelingScenario

Author(s): Eric Stachura

Kennesaw State University

Keywords: traveling waves seepage velocity porous medium

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Abstract

Resource Image Students are taken through a traveling wave analysis of a porous medium model. While the starting point is a nonlinear partial differential equation model, after a change of variables, students are led quickly to an ordinary differential equation model.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

In this scenario, students will be taken through a traveling wave analysis of a porous medium model. While the starting point is a nonlinear partial differential equation (PDE) model, after a change of variables, students are led quickly to an ordinary differential equation (ODE) model. Students will find a power series solution of their ODE. It is expected that students will become familiar with a traveling wave approach to solving PDEs; in particular, they will see how to transform a PDE into an ODE which is easier to solve. At the end, students will think about how to generalize what they have done to other problems.

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Authors

Author(s): Eric Stachura

Kennesaw State University

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