Develop an artificial selective damping stencil for a highorder scheme involving 17 mesh points
7.3. In some applications, a symmetric stencil with regular size mesh may not be the most appropriate. Consider the sevenpoint stencil as shown,
*—— t— *—– t— ¥—– Ф— ¥—– t— *—– t— *
Develop a set of damping coefficients for the stencil.
7.4. In twodimensional problems artificial selective damping is added both in the x and y directions. For instance, the continuity equation with damping terms added
may be written as follows:
(a) Plot contours of constant damping rate in the a Ax – в Ay plane for – n <
a Ax, в Ay < n (assume Ax = Ay).
(b) What is the damping rate for a wave propagating at an angle of 30 degrees to the positive xaxis; the total wave number к Ax = 2.5, where к = (a2 +
в 2)1/2.
7.5. Compute the solution of the convective wave equation
d U d U
T + T – = 0
d t dx
on a uniform mesh with Ax = 1 and the following initial condition,
t = 0, u = [2 + cos(ax)] exp[ (ln 2) (x/10)2]
Consider two cases.
(i) a = 1.7
(ii) a = 4.6
Results to be reported are the spatial distributions of u at t = 400 and t = 800. The exact solution to (i) is
















