Full exam for Mathematical and Numerical Methods in Engineering in the Biomedical Engineering degree programme at Politecnico di Milano. The document covers: Punti:7/33 03/02/21 - MATHEMATICAL AND NUMERICAL METHODS IN ENGINEERING - NUMERICAL PART Prof. P. Zunino TIME : 2h ! Part I Quiz Answer to the following questions: 1 The meaning of CFL condition is that: (1/1 punto) The numerical solution propagates with the same velocity of the
Full exam for Mathematical and Numerical Methods in Engineering in the Biomedical Engineering degree programme at Politecnico di Milano. The document covers: Punti:7/33 03/02/21 - MATHEMATICAL AND NUMERICAL METHODS IN ENGINEERING - NUMERICAL PART Prof. P. Zunino TIME : 2h ! Part I Quiz Answer to the following questions: 1 The meaning of CFL condition is that: (1/1 punto) The numerical solution propagates with the same velocity of the
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Punti:7/33 03/02/21 - MATHEMATICAL AND NUMERICAL METHODS IN ENGINEERING - NUMERICAL PART Prof. P. Zunino TIME : 2h ! Part I Quiz Answer to the following questions: 1 The meaning of CFL condition is that: (1/1 punto) The numerical solution propagates with the same velocity of the analytical one; The numerical solution propagates faster than the analytical one;" It allows to have a null error; The numerical solution propagates slower than the analytical one; 2 Which of the following is the Upwind scheme for a conservation law with convection given by β > 0? (1/1 punto) " =− ( − )+( −2+);/u1D448/u1D45B+1/u1D457/u1D448/u1D45B/u1D457 ∆/u1D461/u1D6FD 2/uni210E/u1D448/u1D45B /u1D457+1/u1D448/u1D45B /u1D457−1 ∆/u1D6FD/u1D461 2/uni210E/u1D448/u1D45B /u1D457+1 /u1D448/u1D45B/u1D457/u1D448/u1D45B /u1D457−1 =− (− )+ ( −2+);/u1D448/u1D45B+1/u1D457/u1D448/u1D45B/u1D457 ∆/u1D461/u1D6FD /uni210E/u1D448/u1D45B/u1D457/u1D448/u1D45B /u1D457−1 ∆/u1D6FD2/u1D4612 2/uni210E2 /u1D448/u1D45B /u1D457+1 /u1D448/u1D45B/u1D457/u1D448/u1D45B /u1D457−1 =(1− )( −);/u1D448/u1D45B+1/u1D457 ∆/u1D461/u1D6FD /uni210E/u1D448/u1D45B /u1D457+1/u1D448/u1D45B/u1D457 =(1− )( − );/u1D448/u1D45B+1/u1D457 ∆/u1D461/u1D6FD /uni210E/u1D448/u1D45B /u1D457+1/u1D448/u1D45B /u1D457−1 # 3 Which sentence is true about the Forward Euler Centered method for the advection problem? (0/1 punto) Requires the solution of a linear system with a symmetric matrix Always (absolute) unstable for any h and ∆t;" Requires the solution of a linear system with a tridiagonal matrix; It is stable and accurate provided that ∆t is small enough; 4 The Backward Euler approximation of the heat equation in algebraic form is given by (A is the matrix related to the approximation of Poisson problem with +2 on the main diagonal and µ the diffusion…
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