Changes between Version 6 and Version 7 of u/ehansen/buildcode


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Timestamp:
10/31/11 18:10:11 (13 years ago)
Author:
ehansen
Comment:

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  • u/ehansen/buildcode

    v6 v7  
    3030Where [[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:
    3131
    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($\int^{x_{i+\frac{1}{2}}}_{x_{i - \frac{1}{2}}} \tilde{U}(x,t^{n+1}) \ \mathrm{d}x = \int^{x_{i+\frac{1}{2}}}_{x_{i - \frac{1}{2}}} \tilde{U}(x,t^{n}) \ \mathrm{d}x \ + \ \int_{t^{n}}^{t^{n+1}}F(x_{i-\frac{1}{2}},t) \ \mathrm{d}t \ - \ \int_{t^{n}}^{t^{n+1}} F(x_{i+\frac{1}{2}},t) \ \mathrm{d}t \ \ \ \ \ (3)$)]]
    3333
    3434