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Q4: The depth averaged velocity field u in a small amplitude oscillation on water of uniform depth h, can be shown to satisfy the wave equation: 0²u əx² where c = √√gh (i) อน at² Derive a finite different explicit scheme for solving this equation, knowing that e is constant and use a uniform space step Ax and time step At. Analyze the scheme, by mentioning what type of boundary or initial conditions are needed, in order to apply it. (ii) If the wave speed is c= 5m/s and Ax= 10m, what is the maximum stable time step?

Q4: The depth averaged velocity field u in a small amplitude oscillation on water of uniform depth h, can be shown to satisfy the wave equation: 0²u əx² where c = √√gh (i) อน at² Derive a finite different explicit scheme for solving this equation, knowing that e is constant and use a uniform space step Ax and time step At. Analyze the scheme, by mentioning what type of boundary or initial conditions are needed, in order to apply it. (ii) If the wave speed is c= 5m/s and Ax= 10m, what is the maximum stable time step?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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Q4: The depth averaged velocity field u in a small amplitude oscillation on water of uniform depth h, can be shown to satisfy the wave equation: where c = √gh (i) อน ət² a²u əx² c². Derive a finite different explicit scheme for solving this equation, knowing that c is constant and use a uniform space step Ax and time step At. Analyze the scheme, by mentioning what type of boundary or initial conditions are needed, in order to apply it. (ii) If the wave speed is c= 5m/s and Ax= 10m, what is the maximum stable time step?
Transcribed Image Text:Q4: The depth averaged velocity field u in a small amplitude oscillation on water of uniform depth h, can be shown to satisfy the wave equation: where c = √gh (i) อน ət² a²u əx² c². Derive a finite different explicit scheme for solving this equation, knowing that c is constant and use a uniform space step Ax and time step At. Analyze the scheme, by mentioning what type of boundary or initial conditions are needed, in order to apply it. (ii) If the wave speed is c= 5m/s and Ax= 10m, what is the maximum stable time step?
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