Q.2. [12 marks] An equation often encountered in the study of numerical algorithms is the so-called 1-d Burgers equation

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Q 2 12 Marks An Equation Often Encountered In The Study Of Numerical Algorithms Is The So Called 1 D Burgers Equation 1 (227.52 KiB) Viewed 38 times

Q.2. [12 marks] An equation often encountered in the study of numerical algorithms is the so-called 1-d Burgers equation; ∂t∂u​+u∂x∂u​=0 This equation originally aroee in the study of the motion of dislocations in metals, but it is often usod in studying the behaviour of numerical algorithms for computing shock waves. We want to solve this equation for the following problem; on a domain 0≤x≤2π, the initial conditions are given by u(x,t=0)=sinx and the boundary conditions are u(x−0,t)=u(x−2π,t)=0; a. Construct an explicit finite difference algorithm to solve the Burger's equation. Use a centered differencing scheme for the spatial derivative. b. Construct in Excel a spreadsheet to solve this problem on a mesh with 20 nodes. Use a Courant number less than 0.25. c. How does the solution evolve from t=0 to t=2.0 ? What is causing the obeerved behaviour, and why might it be interesting to someone studying shocks? (Hint; do some reading around the subject of Burger's equation).