Pertemuan 26
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Transcript of Pertemuan 26
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Parabolic Equation
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Cari u(x,t) yang memenuhi persamaan ParabolikDengan syarat batas u(x,0) = 0 = u(8,t) dan u(x,0) = 4x x2 di x = i : i = 0, 1 , 2 , 3 , 5.
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Solution :c2 = 4 , h = 1, k = 1/8
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Lab 1 DiscussionIn lab 1 we solved the advection equation:
The first method we tried was the forward Euler method:
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Upwind method, CFL=0.9
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Whats Going On?AdvectionDiffusionAdd/subtract
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Numerical DiffusionThe alebgra shows that the finite difference equation has both an advective term and a diffusive term. It is in fact a better model for:
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InstabilityUpwind method, CFL=1.2 (final timstep only)
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Lax-Wendroff method, CFL=0.9
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Flux LimitersIn the advection equation lets assume v is positive:
Most flux limiters are based on the ratio of the first order fluxes at node i, i.e.:
Heat EquationCari u(x,t) yang memenuhi persamaan parabolicC2 = 4 , h = 1, k = 1/8