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ara-prob5 [2021/03/23 08:05] trinh created |
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| + | ====== Monotonic shock solutions ====== | ||
| + | |||
| < | < | ||
| % KS_MONOTONIC_CALLER will solve the K-S equation for the case of the | % KS_MONOTONIC_CALLER will solve the K-S equation for the case of the | ||
| Line 50: | Line 52: | ||
| Yp = [up; upp; uppp]; | Yp = [up; upp; uppp]; | ||
| </ | </ | ||
| + | |||
| + | ====== Oscillatory shock solutions ====== | ||
| + | |||
| + | < | ||
| + | % KS_OSC_CALLER will solve the K-S equation for the case of the | ||
| + | % oscillatory shock conditions | ||
| + | % ------------------------------------------------------------------- | ||
| + | % | ||
| + | % | ||
| + | % | ||
| + | |||
| + | z0 = 1.24; | ||
| + | phi = 2.60586555; | ||
| + | % phi = 2.59; | ||
| + | % phi = 2.5; | ||
| + | |||
| + | ep = 0.05; | ||
| + | zmin = -6; | ||
| + | zmax = 12; | ||
| + | |||
| + | gam = sqrt(1/ep^2 - 1); | ||
| + | bc = @(z) -1 + exp(-(z-z0))*sin(gam*(z-z0)+phi); | ||
| + | |||
| + | bcp = @(z) -exp(-(z-z0))*sin(gam*(z-z0)+phi) + ... | ||
| + | gam*exp(-(z-z0))*cos(gam*(z-z0)+phi); | ||
| + | |||
| + | bcpp = @(z) exp(-(z-z0))*sin(gam*(z-z0)+phi) ... | ||
| + | - 2*gam*exp(-(z-z0))*cos(gam*(z-z0)+phi) ... | ||
| + | -gam^2*exp(-(z-z0))*sin(gam*(z-z0)+phi); | ||
| + | ic = [bc(zmax); ... | ||
| + | bcp(zmax); ... | ||
| + | bcpp(zmax)]; | ||
| + | |||
| + | |||
| + | fwd = @(t,Y) KSode(t, | ||
| + | |||
| + | mytol = 1e-10; | ||
| + | options = odeset(' | ||
| + | sol = ode113(fwd, [zmax, zmin], ic, options); | ||
| + | |||
| + | figure(1) | ||
| + | hold all | ||
| + | plot(sol.x, sol.y(1,: | ||
| + | ylim([-5, | ||
| + | drawnow | ||
| + | </ | ||
| + | |||