Consider the linear advection equation ut + aux = 0. Discretise this equation by the finite difference method, using an explicit Euler discretisation for the ast time derivative, and an upwind discretisation for the space derivative. At what value of the Courant number = - do we have a stable solution with 4x no dispersion and maximum diffusion errors? Give your answer to one decimal place.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Consider the linear advection equation ut +a ux = 0. Discretise this equation by the finite difference method, using an explicit Euler discretisation for the
aAt
time derivative, and an upwind discretisation for the space derivative. At what value of the Courant number o =
do we have a stable solution with
Ax
no dispersion and maximum diffusion errors? Give your answer to one decimal place.
Transcribed Image Text:Consider the linear advection equation ut +a ux = 0. Discretise this equation by the finite difference method, using an explicit Euler discretisation for the aAt time derivative, and an upwind discretisation for the space derivative. At what value of the Courant number o = do we have a stable solution with Ax no dispersion and maximum diffusion errors? Give your answer to one decimal place.
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