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Changed notation of the for loops in the algorithms and fixed incorrect algorithm names

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TechWizzart 2020-09-21 13:50:35 +02:00
parent 9c8baa2cd6
commit 46e5bd6254
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5 changed files with 57 additions and 60 deletions
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8
tex-docs/topics/advection.tex
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@ -54,7 +54,7 @@ With the divergence functon defined in \autoref{alg:divergence}, we now need to
$T_{add} \leftarrow T_a + \delta t \alpha_a \nabla^2(T_a) + \nabla(T_a)$ \;
$T_a \leftarrow T_a + T_{add}[5:-5, :] \text{ //Only add } T_{add} \text{ to } T_a \text{ for indices in the interval } [-nlat + 5, nlat - 5]$. \;
$T_p \leftarrow T_p + \delta t \alpha_p \nabla^2(T_p)$ \;
\caption{The main calculations for calculating the effects of diffusion}
\caption{The main calculations for calculating the effects of advection}
\label{alg:advection}
\end{algorithm}
@ -78,7 +78,7 @@ to calculate $\rho$ after the movement of air has taken place, so we need to cha
$T_a \leftarrow T_a + T_{add}[5:-5, :] \text{ //Only add } T_{add} \text{ to } T_a \text{ for indices in the interval } [-nlat + 5, nlat - 5]$. \;
$\rho \leftarrow \rho + \delta t \nabla \rho$ \;
$T_p \leftarrow T_p + \delta t \alpha_p \nabla^2(T_p)$ \;
\caption{The main calculations for calculating the effects of diffusion}
\caption{The main calculations for calculating the effects of advection}
\label{alg:advectionv2}
\end{algorithm}
@ -92,7 +92,7 @@ boundary.
$T_a \leftarrow T_a - 0.5T_{add}[adv\_bound:-adv\_boun, :] \text{ //Only subtract } T_{add} \text{ to } T_a \text{ for indices in the interval } [-nlat + adv\_boun, nlat - adv\_boun]$. \;
$\rho[adv\_boun: -adv\_boun, :] \leftarrow \rho - 0.5(\delta t \nabla \rho) \text{ //Only change the density for indices in the interval } [-nlat + adv\_boun, nlat - adv\_boun]$ \;
$T_p \leftarrow T_p + \delta t \alpha_p \nabla^2(T_p)$ \;
\caption{The main calculations for calculating the effects of diffusion}
\caption{The main calculations for calculating the effects of advection}
\label{alg:advectionfix}
\end{algorithm}
@ -105,7 +105,7 @@ add it, with \autoref{alg:advection layer} as a result. Here the ':' means all i
$T_a \leftarrow T_a - 0.5T_{add}[adv\_boun:-adv\_boun, :, :] \text{ //Only subtract } T_{add} \text{ to } T_a \text{ for indices in the interval } [-nlat + adv\_boun, nlat - adv\_boun]$. \;
$\rho[adv\_boun: -adv\_boun, :, :] \leftarrow \rho - 0.5(\delta t \nabla \rho) \text{ //Only change the density for indices in the interval } [-nlat + adv\_boun, nlat - adv\_boun]$ \;
$T_p \leftarrow T_p + \delta t \alpha_p \nabla^2(T_p)$ \;
\caption{The main calculations for calculating the effects of diffusion}
\caption{The main calculations for calculating the effects of advection}
\label{alg:advection layer}
\end{algorithm}

2
tex-docs/topics/master.tex
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@ -21,7 +21,7 @@ calculations in \autoref{alg:temperature with density} we would calculate the ve
}
}
}
\caption{Main loop that can simulate flow and advection conditionally}
\caption{Main loop that can simulate velocities and advection conditionally}
\label{alg:stream4v1}
\end{algorithm}

52
tex-docs/topics/radiation.tex
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@ -146,13 +146,13 @@ we change that) amd the current time is obviously not constant. All constants ca
\SetKwInOut{Output}{Output}
\Input{time $t$, amount of energy that hits the planet $S$}
\Output{Temperature of the planet $T_p$, temperature of the atmosphere $T_a$}
\For{$lat \in [-90, 90]$}{
\For{$lon \in [0, 360]$}{
\For{$lat \leftarrow -90$ \KwTo $90$}{
\For{$lon \leftarrow 0$ \KwTo $360$}{
$T_p[lat, lon] \leftarrow T_p[lat, lon] + \frac{\delta t (S + 4\epsilon \sigma (T_a[lat, lon])^4 - 4\sigma (T_p[lat, lon])^4)}{C_p}$ \;
$T_a[lat, lon] \leftarrow T_a[lat, lon] + \frac{\delta t (\sigma (T_p[lat, lon])^4 - 2\epsilon\sigma (T_a[lat, lon])^4)}{C_a}$ \;
}
}
\caption{The main function of the temperature calculations}
\caption{The main function for the temperature calculations}
\label{alg:stream1v1}
\end{algorithm}
@ -197,13 +197,13 @@ that $S$ is defined as the call to \autoref{alg:solar}.
\Input{amount of energy that hits the planet $S$}
\Output{Temperature of the planet $T_p$, temperature of the atmosphere $T_a$}
\For{$lat \in [-nlat, nlat]$}{
\For{$lon \in [0, nlot]$}{
\For{$lat \leftarrow -nlat$ \KwTo $nlat$}{
\For{$lon \leftarrow 0$ \KwTo $nlot$}{
$T_p[lat, lon] \leftarrow T_p[lat, lon] + \frac{\delta t (S + 4\epsilon \sigma (T_a[lat, lon])^4 - 4\sigma (T_p[lat, lon])^4)}{C_p}$ \;
$T_a[lat, lon] \leftarrow T_a[lat, lon] + \frac{\delta t (\sigma (T_p[lat, lon])^4 - 2\epsilon\sigma (T_a[lat, lon])^4)}{C_a}$ \;
}
}
\caption{The main function of the temperature calculations}
\caption{The main function for the temperature calculations}
\label{alg:stream1v2}
\end{algorithm}
@ -229,13 +229,13 @@ reflected instead of absorbed, where we need the amount that is absorbed which i
\SetKwInOut{Output}{Output}
\Input{amount of energy that hits the planet $S$}
\Output{Temperature of the planet $T_p$, temperature of the atmosphere $T_a$}
\For{$lat \in [-nlat, nlat]$}{
\For{$lon \in [0, nlot]$}{
\For{$lat \leftarrow -nlat$ \KwTo $nlat$}{
\For{$lon \leftarrow 0$ \KwTo $nlot$}{
$T_p[lat, lon] \leftarrow T_p[lat, lon] + \frac{\delta t ((1 - a[lat, lon])S + 4\epsilon \sigma (T_a[lat, lon])^4 - 4\sigma (T_p[lat, lon])^4)}{C_p[lat, lon]}$ \;
$T_a[lat, lon] \leftarrow T_a[lat, lon] + \frac{\delta t (\sigma (T_p[lat, lon])^4 - 2\epsilon\sigma (T_a[lat, lon])^4)}{C_a}$ \;
}
}
\caption{The main loop of the temperature calculations}
\caption{The main function for the temperature calculations}
\label{alg:stream2v3}
\end{algorithm}
@ -249,13 +249,13 @@ The air density is not at all points exactly the same. This may be due to the wi
\SetKwInOut{Output}{Output}
\Input{amount of energy that hits the planet $S$}
\Output{Temperature of the planet $T_p$, temperature of the atmosphere $T_a$}
\For{$lat \in [-nlat, nlat]$}{
\For{$lon \in [0, nlot]$}{
\For{$lat \leftarrow -nlat$ \KwTo $nlat$}{
\For{$lon \leftarrow 0$ \KwTo $nlot$}{
$T_p[lat, lon] \leftarrow T_p[lat, lon] + \frac{\delta t ((1 - a[lat, lon])S + 4\epsilon \sigma (T_a[lat, lon])^4 - 4\sigma (T_p[lat, lon])^4)}{\rho[lat, lon]C_p[lat, lon]}$ \;
$T_a[lat, lon] \leftarrow T_a[lat, lon] + \frac{\delta t (\sigma (T_p[lat, lon])^4 - 2\epsilon\sigma (T_a[lat, lon])^4)}{\rho[lat, lon]C_a}$ \;
}
}
\caption{The main loop of the temperature calculations}
\caption{The main function for the temperature calculations}
\label{alg:temperature with density}
\end{algorithm}
@ -294,15 +294,15 @@ regards to the storage of the values) by the addition of multiple atmospheric la
\SetKwInOut{Output}{Output}
\Input{amount of energy that hits the planet $S$}
\Output{Temperature of the planet $T_p$, temperature of the atmosphere $T_a$}
\For{$lat \in [-nlat, nlat]$}{
\For{$lon \in [0, nlot]$}{
\For{$layer \in [0, nlevels]$}{
\For{$lat \leftarrow -nlat$ \KwTo $nlat$}{
\For{$lon \leftarrow 0$ \KwTo $nlot$}{
\For{$layer \leftarrow 0$ \KwTo $nlevels$}{
$T_p[lat, lon] \leftarrow T_p[lat, lon] + \frac{\delta t ((1 - a[lat, lon])S + \sigma(4\epsilon[0](T_a[lat, lon, 0])^4 - 4(T_p[lat, lon])^4))}
{4C_p[lat, lon]}$ \;
\uIf{$layer == 0$}{
\uIf{$layer = 0$}{
$T_a[lat, lon, layer] \leftarrow T_a[lat, lon, layer] + \frac{\delta t \sigma((T_p[lat, lon])^4 - 2\epsilon[layer](T_a[lat, lon, layer])^4)}
{\rho[lat, lon, layer]C_a\delta z[layer]}$ \;
}\uElseIf{$layer == nlevels - 1$}{
}\uElseIf{$layer = nlevels - 1$}{
$T_a[lat, lon, layer] \leftarrow T_a[lat, lon, layer] + \frac{\delta t \sigma(\epsilon[layer - 1](T_a[lat, lon, layer - 1])^4 - 2\epsilon[layer](T_a[lat, lon, layer])^4)}
{\rho[lat, lon, layer]C_a\delta z[layer]}$ \;
}\uElse{
@ -312,7 +312,7 @@ regards to the storage of the values) by the addition of multiple atmospheric la
}
}
}
\caption{The main loop of the temperature calculations}
\caption{The main function for the temperature calculations}
\label{alg:temperature layer}
\end{algorithm}
@ -320,7 +320,7 @@ We also need to initialise the $\epsilon$ value for each layer. We do that in \a
\begin{algorithm}
$\epsilon[0] \leftarrow 0.75$ \;
\For{$i \in [1, nlevels]$}{
\For{$i \leftarrow 1$ \KwTo $nlevels$}{
$\epsilon[i] \leftarrow 0.5\epsilon[i - 1]$
}
\caption{Intialisation of the insulation of each layer (also known as $\epsilon$)}
@ -406,23 +406,23 @@ $S_z$ represents the call to \autoref{alg:gradient z}. \texttt{solar} represents
\SetKwInOut{Output}{Output}
\Input{amount of energy that hits the planet $S$}
\Output{Temperature of the planet $T_p$, temperature of the atmosphere $T_a$}
\For{$lat \in [-nlat, nlat]$}{
\For{$lon \in [0, nlon]$}{
\For{$lat \leftarrow -nlat$ \KwTo $nlat$}{
\For{$lon \leftarrow 0$ \KwTo $nlot$}{
$pressureProfile \leftarrow p[lat, lon, :]$ \;
$\tau = \tau_0(lat)f_l\frac{pressureProfile}{pressureProfile[0]} + (1 - f_l)(\frac{pressureProfile}{pressureProfile[0]})^4)$ \;
$U[0] \leftarrow \sigma T_p[lat, lon]^4$ \;
\For{$level \in [1, nlevels]$}{
\For{$level \leftarrow 1$ \KwTo $nlevels$}{
$U[level] \leftarrow U[level - 1] - \frac{(\tau[level] - \tau[level - 1])(\sigma \cdot (mean(T_a[:, :, level]))^4)}{1 + (\tau[level - 1] - \tau[level])}$ \;
}
$D[nlevels - 1] \leftarrow 0$ \;
\For{$level \in [nlevels - 1, 0]$}{
\For{$level \leftarrow nleves - 1$ \KwTo $0$}{
$D[level] \leftarrow D[level + 1] - \frac{(\tau[level + 1] - \tau[level])(\sigma \cdot (mean(T_a[:, :, level]))^4)}{1 + (\tau[level] - \tau[level + 1])}$ \;
}
\For{$level \in [0, nlevels]$}{
\For{$level \leftarrow 0$ \KwTo $nlevels$}{
$Q[level] \leftarrow - \frac{S_z(U - D, 0, 0, level)}{10^3 \cdot densityProfile[level]}$ \;
}
@ -433,7 +433,7 @@ $S_z$ represents the call to \autoref{alg:gradient z}. \texttt{solar} represents
$T_p[lat, lon] \leftarrow T_p[lat, lon] \frac{\delta t((1 - a[lat, lon]) S + S_z(D, 0, 0, 0) - \sigma T_p[lat, lon]^4)}{C_p[lat ,lon]}$ \;
}
}
\caption{Adding in radiation}
\caption{Main function for calculating the temperature using radiation}
\label{alg:optical depth}
\end{algorithm}
@ -450,7 +450,7 @@ $Q$. We add in a check to see if we are currently calculating the radiation in t
height.
\begin{algorithm}
\For{$level \in [0, nlevels]$}{
\For{$level \leftarrow 0$ \KwTo $nlevels$}{
$Q[level] \leftarrow - \frac{S_z(U - D, 0, 0, level)}{10^3 \cdot densityProfile[level]}$ \;
\uIf{$heights[level] > 20 \cdot 10^3$}{
$Q[level] \leftarrow Q[level] + \texttt{solar}(5, lat, lon, t) \frac{24 \cdot 60 \cdot 60(\frac{heights[level] - 20 \cdot 10^3}{10^3})^2}{30^2}$ \;

43
tex-docs/topics/util_funcs.tex
View File

@ -23,7 +23,7 @@ calculations we will do later on.
\SetKwInOut{Output}{Output}
\Input{Matrix (double array) $a$, first index $i$, second index $j$, third index $k$ with default value \texttt{NULL}}
\Output{Gradient in the $x$ direction}
\eIf{$k == \texttt{NULL}$}{
\eIf{$k = \texttt{NULL}$}{
$grad \leftarrow \frac{a[i, (j + 1)\text{ mod } nlon] - a[i, (j - 1) \text{ mod } nlon]}{\delta x[i]}$ \;
}{
$grad \leftarrow \frac{a[i, (j + 1)\text{ mod } nlon, k] - a[i, (j - 1) \text{ mod } nlon, k]}{\delta x[i]}$ \;
@ -38,18 +38,18 @@ calculations we will do later on.
\SetKwInOut{Output}{Output}
\Input{Matrix (double array) $a$, first index $i$, second index $j$, third index $k$ with default value \texttt{NULL}}
\Output{Gradient in the $y$ direction}
\eIf{$k == \texttt{NULL}$}{
\eIf{$k = \texttt{NULL}$}{
\uIf{$i == 0$}{
$grad \leftarrow 2 \frac{a[i + 1, j] - a[i, j]}{\delta y}$ \;
}\uElseIf{$i == nlat - 1$}{
}\uElseIf{$i = nlat - 1$}{
$grad \leftarrow 2 \frac{a[i, j] - a[i - 1, j]}{\delta y}$ \;
}\uElse{
$grad \leftarrow \frac{a[i + 1, j] - a[i - 1 j]}{\delta y}$ \;
}
}{
\uIf{$i == 0$}{
\uIf{$i = 0$}{
$grad \leftarrow 2 \frac{a[i + 1, j, k] - a[i, j, k]}{\delta y}$ \;
}\uElseIf{$i == nlat - 1$}{
}\uElseIf{$i = nlat - 1$}{
$grad \leftarrow 2 \frac{a[i, j, k] - a[i - 1, j, k]}{\delta y}$ \;
}\uElse{
$grad \leftarrow \frac{a[i + 1, j] - a[i - 1 j]}{\delta y}$ \;
@ -65,18 +65,18 @@ calculations we will do later on.
\SetKwInOut{Output}{Output}
\Input{Matrix (double array) $a$, first index $i$, second index $j$, third index $k$}
\Output{Gradient in the $z$ direction}
\uIf{$a.dimensions == 1$}{
\uIf{$k == 0$}{
\uIf{$a.dimensions = 1$}{
\uIf{$k = 0$}{
$grad \leftarrow \frac{a[k + 1] - a[k]}{\delta z[k]}$ \;
}\uElseIf{$k == nlevels - 1$}{
}\uElseIf{$k = nlevels - 1$}{
$grad \leftarrow \frac{a[k] - a[k - 1]}{\delta z[k]}$ \;
}\uElse{
$grad \leftarrow \frac{a[k + 1] - a[k - 1]}{2\delta z[k]}$ \;
}
} \uElse {
\uIf{$k == 0$}{
\uIf{$k = 0$}{
$grad \leftarrow \frac{a[i, j, k + 1] - a[i, j, k]}{\delta z[k]}$ \;
}\uElseIf{$k == nlevels - 1$}{
}\uElseIf{$k = nlevels - 1$}{
$grad \leftarrow \frac{a[i, j, k] - a[i, j, k - 1]}{\delta z[k]}$ \;
}\uElse{
$grad \leftarrow \frac{a[i, j, k + 1] - a[i, j, k - 1]}{2\delta z[k]}$ \;
@ -131,17 +131,17 @@ respectively.
\SetKwInOut{Output}{Output}
\Input{A matrix (double array) a}
\Output{A matrix (double array) with results for the laplacian operator for each element}
\eIf{$a.dimensions == 2$}{
\For{$lat \in [1, nlat - 1]$}{
\For{$lon \in [0, nlon]$}{
\eIf{$a.dimensions = 2$}{
\For{$lat \leftarrow 1$ \KwTo $nlat - 1$}{
\For{$lon \leftarrow 0$ \KwTo $nlon$}{
$output[lat, lon] \leftarrow \frac{\Delta_x(a, lat, (lon + 1) \text{ mod } nlon) - \Delta_x(a, lat, (lon - 1) \text{ mod } nlon)}{\delta x[lat]} + \frac{\Delta_y(a, lat + 1, lon) -
\Delta_y(a, lat - 1, lon)}{\delta y}$\;
}
}
}{
\For{$lat \in [1, nlat - 1]$}{
\For{$lon \in [0, nlon]$}{
\For{$k \in [0, nlevels - 1]$}{
\For{$lat \leftarrow 1$ \KwTo $nlat - 1$}{
\For{$lon \leftarrow 0$ \KwTo $nlon$}{
\For{$k \leftarrow 0$ \KwTo $nlevels - 1$}{
$output[lat, lon, k] \leftarrow \frac{\Delta_x(a, lat, (lon + 1) \text{ mod } nlon, k) - \Delta_x(a, lat, (lon - 1) \text{ mod } nlon, k)}{\delta x[lat]} + \frac{\Delta_y(a,
lat + 1, lon, k) - \Delta_y(a, lat - 1, lon, k)}{\delta y} + \frac{\Delta_z(a, lat, lon, k + 1) - \Delta_z(a, lat, lon, k + 1)}{2\delta z[k]}$\;
}
@ -164,12 +164,9 @@ as we expect that we might use it in combination with the divergence operator mo
\SetKwInOut{Output}{Output}
\Input{A matrix (double array) $a$}
\Output{A matrix (double array) containing the result of the divergence operator taken over that element}
$dim_1 \leftarrow \text{ Length of } a \text{ in the first dimension}$ \;
\For{$i \in [0, dim_1]$}{
$dim_2 \leftarrow \text{ Length of } a \text{ in the second dimension (i.e. the length of the array stored at index } i)$ \;
\For{$j \in [0, dim_2]$}{
$dim_3 \leftarrow \text{ Length of } a \text{ in the third dimension}$ \;
\For{$k \in [0, dim_3]$}{
\For{$i \leftarrow 0$ \KwTo $a.length$}{
\For{$j \leftarrow 0$ \KwTo $a[i].length$}{
\For{$k \leftarrow 0$ \KwTo $a[i, j].length$}{
$output[i, j, k] \leftarrow \Delta_x(au, i, j, k) + \Delta_y(av, i, j, k) + \Delta_z(aw, i, j, k)$ \;
}
}
@ -275,7 +272,7 @@ This symmetry as it is called can be exploited to produce a divide and conquer a
} \uElse{
$B[0], \dots, B[\frac{N}{2} - 1] \leftarrow \texttt{FFT}(A, i, \frac{N}{2}, 2s)$ \;
$B[\frac{N}{2}], \dots, B[N - 1] \leftarrow \texttt{FFT}(A, i + s, \frac{N}{2}, 2s)$ \;
\For{$k = 0$ to $\frac{N}{2} - 1$}{
\For{$k \leftarrow 0$ \KwTo $\frac{N}{2} - 1$}{
$t \leftarrow B[k]$ \;
$B[k] \leftarrow t + e^{-2i\pi \frac{k}{N}} B[k + \frac{N}{2}]$ \;
$B[k + \frac{N}{2}] \leftarrow t - e^{-2i\pi \frac{k}{N}} B[k + \frac{N}{2}]$ \;

12
tex-docs/topics/velocity.tex
View File

@ -98,8 +98,8 @@ With the gradient functions defined in \autoref{alg:gradient x} and \autoref{alg
$S_{yv} \leftarrow \texttt{gradient\_y}(v, lan, lon)$ \;
$S_{px} \leftarrow \texttt{gradient\_x}(p, lan, lon)$ \;
$S_{py} \leftarrow \texttt{gradient\_x}(p, lan, lon)$ \;
\For{$lat \in [1, nlat - 1]$}{
\For{$lon \in [0, nlon]$}{
\For{$lat \leftarrow 1$ \KwTo $nlat - 1$}{
\For{$lon \leftarrow 0$ \KwTo $nlon$}{
$u[lan, lon] \leftarrow u[lan, lon] + \delta t \frac{-u[lan, lon]S_{xu} - v[lan, lon]S_{yu} + f[lan]v[lan, lon] - S_{px}}{\rho}$ \;
$v[lan, lon] \leftarrow v[lan, lon] + \delta t \frac{-u[lan, lon]S_{xv} - v[lan, lon]S_{yv} - f[lan]u[lan, lon] - S_{py}}{\rho}$ \;
}
@ -116,7 +116,7 @@ Another change introduced is in the coriolis parameter. Up until now it has been
\SetAlgoLined
$\Omega \leftarrow 7.2921 \cdot 10^{-5}$ \;
\For{$lat \in [-nlat, nlat]$}{
\For{$lat \leftarrow -nlat$ \KwTo $nlat$}{
$f[lat] \leftarrow 2\Omega \sin(lat \frac{\pi}{180})$ \;
}
\caption{Calculating the coriolis force}
@ -141,9 +141,9 @@ then so does $y$.}
$S_{yv} \leftarrow \texttt{gradient\_y}(v, lan, lon)$ \;
$S_{px} \leftarrow \texttt{gradient\_x}(p, lan, lon)$ \;
$S_{py} \leftarrow \texttt{gradient\_y}(p, lan, lon)$ \;
\For{$lat \in [1, nlat - 1]$}{
\For{$lon \in [0, nlon]$}{
\For{$layer \in [0, nlevels]$}{
\For{$lat \leftarrow 1$ \KwTo $nlat - 1$}{
\For{$lon \leftarrow 0$ \KwTo $nlon$}{
\For{$layer \leftarrow 0$ \KwTo $nlevels$}{
$u[lan, lon, layer] \leftarrow u[lat, lon, layer] + \delta t \frac{-u[lat, lon, layer]S_{xu} - v[lat, lon, layer]S_{yu} + f[lat]v[lat, lon, layer] - S_{px}}{\rho}$ \;
$v[lan, lon, layer] \leftarrow v[lat, lon, layer] + \delta t \frac{-u[lat, lon, layer]S_{xv} - v[lat, lon, layer]S_{yv} - f[lat]u[lat, lon, layer] - S_{py}}{\rho}$ \;
$w[lan, lon, layer] \leftarrow w[lat, lon, layer] - \frac{p[lat, lon, layer] - p_o[lat, lon, layer]}{\delta t\rho[lat, lon, layer]g}$ \;