Changes between Version 6 and Version 7 of u/ehansen/buildcode
- Timestamp:
- 10/31/11 18:10:11 (13 years ago)
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u/ehansen/buildcode
v6 v7 30 30 Where [[latex($\tilde{U}$)]] is the global solution as opposed to the local solution [[latex($U$)]]. However, we already know that the global solution can be written in terms of its fluxes. You just use equation (1) with a specific control volume: 31 31 32 [[latex($\int^{x_{i+\frac{1}{2}}}_{x_{i - \frac{1}{2}}} \tilde{U}(x,t^{n+1}) \ \mathrm{d}x = \int^{x_{i+\frac{1}{2}}}_{x_{i - \frac{1}{2}}} \tilde{U}(x,t^{n}) \ \mathrm{d}x + \int_{t^{n}}^{t^{n+1}}F(x_{i-\frac{1}{2}},t) \ \mathrm{d}t -\int_{t^{n}}^{t^{n+1}} F(x_{i+\frac{1}{2}},t) \ \mathrm{d}t \ \ \ \ \ (3)$)]]32 [[latex($\int^{x_{i+\frac{1}{2}}}_{x_{i - \frac{1}{2}}} \tilde{U}(x,t^{n+1}) \ \mathrm{d}x = \int^{x_{i+\frac{1}{2}}}_{x_{i - \frac{1}{2}}} \tilde{U}(x,t^{n}) \ \mathrm{d}x \ + \ \int_{t^{n}}^{t^{n+1}}F(x_{i-\frac{1}{2}},t) \ \mathrm{d}t \ - \ \int_{t^{n}}^{t^{n+1}} F(x_{i+\frac{1}{2}},t) \ \mathrm{d}t \ \ \ \ \ (3)$)]] 33 33 34 34