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Pertemuan 26

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:

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Pertemuan 26

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  1. Pertemuan 26 Parabolic Equation

  2. Cari u(x,t) yang memenuhi persamaan Parabolik Dengan syarat batas u(x,0) = 0 = u(8,t) dan u(x,0) = 4x – ½ x2 di x = i : i = 0, 1 , 2 , 3 ,… 5.

  3. Solution : c2 = 4 , h = 1, k = 1/8

  4. Lab 1 Discussion • In lab 1 we solved the advection equation: • The first method we tried was the forward Euler method:

  5. Upwind method, CFL=0.9

  6. What’s Going On? Add/subtract Advection Diffusion

  7. Numerical Diffusion • The alebgra shows that the finite difference equation has both an advective term and a diffusive term. It is in fact a better model for:

  8. Instability Upwind method, CFL=1.2 (final timstep only)

  9. Lax-Wendroff method, CFL=0.9

  10. Flux Limiters • In the advection equation let’s assume v is positive: • Most flux limiters are based on the ratio of the first order fluxes at node i, i.e.:

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