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Jingru923 committed Jul 16, 2024
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40 changes: 20 additions & 20 deletions concept/allocation.html
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Expand Up @@ -588,7 +588,7 @@ <h2 data-number="4.3" class="anchored" data-anchor-id="the-optimization-constrai
<section id="example" class="level2" data-number="4.4">
<h2 data-number="4.4" class="anchored" data-anchor-id="example"><span class="header-section-number">4.4</span> Example</h2>
<p>The following is an example of an optimization problem for the example shown <a href="../guide/examples.html#model-with-allocation-user-demand">here</a>:</p>
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<summary>Code</summary>
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">Ribasim</span></span>
Expand All @@ -611,39 +611,39 @@ <h2 data-number="4.4" class="anchored" data-anchor-id="example"><span class="hea
<span id="cb1-18"><a href="#cb1-18" aria-hidden="true" tabindex="-1"></a><span class="fu">println</span>(p.allocation.allocation_models[<span class="fl">1</span>].problem)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<pre><code>Min F[(Basin #5, UserDemand #6)]² + F[(Basin #2, UserDemand #3)]² + F[(Basin #12, UserDemand #13)]²
<pre><code>Min F[(Basin #5, UserDemand #6)]² + F[(Basin #12, UserDemand #13)]² + F[(Basin #2, UserDemand #3)]²
Subject to
source[(FlowBoundary #1, Basin #2)] : F[(FlowBoundary #1, Basin #2)] ≤ 172800
source_user[UserDemand #6] : F[(UserDemand #6, Basin #5)] ≤ 0
source_user[UserDemand #13] : F[(UserDemand #13, Terminal #10)] ≤ 0
source_user[UserDemand #3] : F[(UserDemand #3, Basin #2)] ≤ 0
fractional_flow[(TabulatedRatingCurve #7, FractionalFlow #8)] : -0.6 F[(Basin #5, TabulatedRatingCurve #7)] + F[(TabulatedRatingCurve #7, FractionalFlow #8)] ≤ 0
source_user[UserDemand #13] : F[(UserDemand #13, Terminal #10)] ≤ 0
source_user[UserDemand #6] : F[(UserDemand #6, Basin #5)] ≤ 0
fractional_flow[(TabulatedRatingCurve #7, FractionalFlow #8)] : F[(TabulatedRatingCurve #7, FractionalFlow #8)] - 0.6 F[(Basin #5, TabulatedRatingCurve #7)] ≤ 0
fractional_flow[(TabulatedRatingCurve #7, FractionalFlow #9)] : -0.4 F[(Basin #5, TabulatedRatingCurve #7)] + F[(TabulatedRatingCurve #7, FractionalFlow #9)] ≤ 0
flow_buffer_outflow[TabulatedRatingCurve #7] : F_flow_buffer_out[TabulatedRatingCurve #7] ≤ 0
flow_conservation[Basin #2] : F[(FlowBoundary #1, Basin #2)] - F[(Basin #2, UserDemand #3)] - F[(Basin #2, LinearResistance #4)] + F[(LinearResistance #4, Basin #2)] + F[(UserDemand #3, Basin #2)] = 0
flow_conservation[FractionalFlow #9] : -F[(FractionalFlow #9, Basin #12)] + F[(TabulatedRatingCurve #7, FractionalFlow #9)] = 0
flow_conservation[Basin #12] : F[(FractionalFlow #9, Basin #12)] - F[(Basin #12, UserDemand #13)] = 0
flow_conservation[Terminal #10] : F[(FractionalFlow #8, Terminal #10)] + F[(UserDemand #13, Terminal #10)] = 0
flow_conservation[Basin #5] : -F[(Basin #5, TabulatedRatingCurve #7)] - F[(Basin #5, UserDemand #6)] + F[(UserDemand #6, Basin #5)] + F[(LinearResistance #4, Basin #5)] - F[(Basin #5, LinearResistance #4)] = 0
flow_conservation[Basin #2] : -F[(Basin #2, LinearResistance #4)] + F[(LinearResistance #4, Basin #2)] + F[(FlowBoundary #1, Basin #2)] + F[(UserDemand #3, Basin #2)] - F[(Basin #2, UserDemand #3)] = 0
flow_conservation[Basin #5] : -F[(Basin #5, UserDemand #6)] + F[(UserDemand #6, Basin #5)] + F[(LinearResistance #4, Basin #5)] - F[(Basin #5, LinearResistance #4)] - F[(Basin #5, TabulatedRatingCurve #7)] = 0
flow_conservation[Terminal #10] : F[(UserDemand #13, Terminal #10)] + F[(FractionalFlow #8, Terminal #10)] = 0
flow_conservation[FractionalFlow #8] : -F[(FractionalFlow #8, Terminal #10)] + F[(TabulatedRatingCurve #7, FractionalFlow #8)] = 0
flow_conservation[LinearResistance #4] : F[(Basin #2, LinearResistance #4)] - F[(LinearResistance #4, Basin #2)] - F[(LinearResistance #4, Basin #5)] + F[(Basin #5, LinearResistance #4)] = 0
flow_conservation[TabulatedRatingCurve #7] : F[(Basin #5, TabulatedRatingCurve #7)] - F[(TabulatedRatingCurve #7, FractionalFlow #9)] - F[(TabulatedRatingCurve #7, FractionalFlow #8)] - F_flow_buffer_in[TabulatedRatingCurve #7] + F_flow_buffer_out[TabulatedRatingCurve #7] = 0
F[(Basin #5, TabulatedRatingCurve #7)] ≥ 0
F[(FlowBoundary #1, Basin #2)] ≥ 0
flow_conservation[FractionalFlow #9] : -F[(FractionalFlow #9, Basin #12)] + F[(TabulatedRatingCurve #7, FractionalFlow #9)] = 0
flow_conservation[TabulatedRatingCurve #7] : -F[(TabulatedRatingCurve #7, FractionalFlow #8)] + F[(Basin #5, TabulatedRatingCurve #7)] - F[(TabulatedRatingCurve #7, FractionalFlow #9)] - F_flow_buffer_in[TabulatedRatingCurve #7] + F_flow_buffer_out[TabulatedRatingCurve #7] = 0
flow_conservation[Basin #12] : -F[(Basin #12, UserDemand #13)] + F[(FractionalFlow #9, Basin #12)] = 0
F[(Basin #5, UserDemand #6)] ≥ 0
F[(FractionalFlow #8, Terminal #10)] ≥ 0
F[(Basin #2, UserDemand #3)] ≥ 0
F[(Basin #2, LinearResistance #4)] ≥ 0
F[(LinearResistance #4, Basin #2)] ≥ 0
F[(UserDemand #3, Basin #2)] ≥ 0
F[(UserDemand #6, Basin #5)] ≥ 0
F[(FractionalFlow #9, Basin #12)] ≥ 0
F[(TabulatedRatingCurve #7, FractionalFlow #9)] ≥ 0
F[(FlowBoundary #1, Basin #2)] ≥ 0
F[(UserDemand #13, Terminal #10)] ≥ 0
F[(Basin #12, UserDemand #13)] ≥ 0
F[(UserDemand #6, Basin #5)] ≥ 0
F[(LinearResistance #4, Basin #5)] ≥ 0
F[(Basin #5, LinearResistance #4)] ≥ 0
F[(FractionalFlow #8, Terminal #10)] ≥ 0
F[(TabulatedRatingCurve #7, FractionalFlow #8)] ≥ 0
F[(UserDemand #13, Terminal #10)] ≥ 0
F[(FractionalFlow #9, Basin #12)] ≥ 0
F[(UserDemand #3, Basin #2)] ≥ 0
F[(Basin #5, TabulatedRatingCurve #7)] ≥ 0
F[(TabulatedRatingCurve #7, FractionalFlow #9)] ≥ 0
F[(Basin #2, UserDemand #3)] ≥ 0
F_flow_buffer_in[TabulatedRatingCurve #7] ≥ 0
F_flow_buffer_out[TabulatedRatingCurve #7] ≥ 0
</code></pre>
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4 changes: 2 additions & 2 deletions concept/modelconcept.html
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Expand Up @@ -319,9 +319,9 @@ <h2 data-number="1.1" class="anchored" data-anchor-id="water-balance-equations">
<p><span class="math display">\[
\frac{\mathrm{d}S}{\mathrm{d}t} = Q_{in} - Q_{out}
\]</span></p>
<p>We can split out the fluxes into separate terms, such as precipitation <span class="math inline">\(P\)</span>, evapotranspiration <span class="math inline">\(ET\)</span> and runoff <span class="math inline">\(R\)</span>. For now other fluxes are combined into <span class="math inline">\(Q_{rest}\)</span>. If we define all fluxes entering our reservoir as positive, and those leaving the system as negative, all fluxes can be summed up.</p>
<p>We can split out the fluxes into separate terms, such as precipitation <span class="math inline">\(P\)</span> and evapotranspiration <span class="math inline">\(ET\)</span>. For now other fluxes are combined into <span class="math inline">\(Q_{rest}\)</span>. If we define all fluxes entering our reservoir as positive, and those leaving the system as negative, all fluxes can be summed up.</p>
<p><span class="math display">\[
\frac{\mathrm{d}S}{\mathrm{d}t} = R + P + ET + Q_{rest}
\frac{\mathrm{d}S}{\mathrm{d}t} = P + ET + Q_{rest}
\]</span></p>
</section>
<section id="time" class="level2" data-number="1.2">
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