03 02 21

Pagina 1

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…