Burgers equation with constant wave velocity: u/t + c u/x = 2 u/x 2 where c=1,
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Question:
Burgers equation with constant wave velocity:
∂u/∂t + c ∂u/∂x = ∂2u/∂x2
where c=1, v=0.1, 0
Initial condition: u(x,0)-sin(x); periodic boundary condition: u(0,t)-(2,)
Questions:
(1) Apply Fourier stability analysis to show its G factor.
2) Based on the G factor from Q1, if Δ = 0.01, choose a proper range of Ar and make sure the explicit difference equation is conditionally stable.
(3) Choose Ar=0.01 and Δ=0.01, calculate the distribution of u(x) ∈ [0,2].
4) Now if we choose the wave speed c-u, please repeat Q1 to Q3.
Related Book For
Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell
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