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Pertemuan 26. Parabolic Equation. Cari u(x,t) yang memenuhi persamaan Parabolik. Dengan syarat batas u(x,0) = 0 = u(8,t) dan u(x,0) = 4x – ½ x 2 di x = i : i = 0, 1 , 2 , 3 ,… 5. Solution :. c 2 = 4 , h = 1, k = 1/8 . Lab 1 Discussion. In lab 1 we solved the advection equation: - PowerPoint PPT Presentation
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Parabolic Equation
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.
Solution :c2 = 4 , h = 1, k = 1/8
Lab 1 DiscussionIn lab 1 we solved the advection equation:
The first method we tried was the forward Euler method:
Upwind method, CFL=0.9
Whats Going On?AdvectionDiffusionAdd/subtract
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:
InstabilityUpwind method, CFL=1.2 (final timstep only)
Lax-Wendroff method, CFL=0.9
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