| 1 | package myShallowRiver
|
|---|
| 2 | // Package for simulating a Shallow River
|
|---|
| 3 | // author: Bernt Lie
|
|---|
| 4 | // Telemark University College
|
|---|
| 5 | // September 10, 2013
|
|---|
| 6 | model compareShallowRiver
|
|---|
| 7 | simShallowRiver sr5(NVd = 5),sr10(NVd = 10),sr20(NVd = 20); //,sr50(NVd = 50);
|
|---|
| 8 | end compareShallowRiver;
|
|---|
| 9 | //
|
|---|
| 10 | model simShallowRiver
|
|---|
| 11 | // Main Shallow River model
|
|---|
| 12 | // author: Bernt Lie
|
|---|
| 13 | // Telemark University College
|
|---|
| 14 | // September 10, 2013
|
|---|
| 15 | //
|
|---|
| 16 | // Constants
|
|---|
| 17 | constant Real g = 9.81 "Gravity, m/s2";
|
|---|
| 18 | // Parameters
|
|---|
| 19 | parameter Real w = 100 "River width, m";
|
|---|
| 20 | parameter Real L = 5e3 "River length, m";
|
|---|
| 21 | parameter Real H = 57 "River bed drop, m";
|
|---|
| 22 | parameter Real th = asin(H/L) "River bed angle, rad";
|
|---|
| 23 | parameter Real rho = 1e3 "Density of water, kg/m3";
|
|---|
| 24 | parameter Real kS = 20 "Strickler's friction factor, m0.33/s";
|
|---|
| 25 | parameter Integer NVd = 18 "Number of momentum balance segments, -";
|
|---|
| 26 | parameter Real dx = L/NVd "discretization step, m";
|
|---|
| 27 | parameter Real oneh[NVd+1] = ones(NVd+1);
|
|---|
| 28 | // Initial state parameters
|
|---|
| 29 | parameter Real h0 = 4;// 0.5275 "Initial guess river level, m";
|
|---|
| 30 | parameter Real Vd0 = 120 "Initial guess volumetric flow rate, m3/s";
|
|---|
| 31 | // Declaring variables
|
|---|
| 32 | // -- states
|
|---|
| 33 | Real h[NVd+1](each start = h0); //, each fixed = true) "Level states, m";
|
|---|
| 34 | Real Vd[NVd](each start = Vd0); //, each fixed = true) "Volumetric flow rates, m3/s";
|
|---|
| 35 | // -- auxiliary variables at mass knots
|
|---|
| 36 | Real A[NVd+1] "Area perpendicular to flow direction, m2";
|
|---|
| 37 | Real per[NVd+1] "Wetting perimeter, m";
|
|---|
| 38 | // -- auxiliary variables at momentum knots
|
|---|
| 39 | Real h_[NVd] "Staggered levels, m";
|
|---|
| 40 | Real A_[NVd] "Staggered areas, m2";
|
|---|
| 41 | Real Md_rho_i[NVd] "Input momentum flow/density, m4/s2";
|
|---|
| 42 | Real Md_rho_o[NVd] "Output momentum flow/density, m4/s2";
|
|---|
| 43 | Real per_[NVd] "Staggered wetted perimeters, m";
|
|---|
| 44 | Real R_[NVd] "Staggered hydraulic radii, m";
|
|---|
| 45 | Real C_[NVd] "Staggered Chezy coefficient, ...";
|
|---|
| 46 | // Real vMd[NVd] "stupid vector";
|
|---|
| 47 | // Real vp[NVd] "stupid vector";
|
|---|
| 48 | // Real vg[NVd] "stupid vector";
|
|---|
| 49 | // Real vf[NVd] "stupid vector";
|
|---|
| 50 | Real vMdip[NVd-2] "stupid vector";
|
|---|
| 51 | Real vMdim[NVd-2] "stupid vector";
|
|---|
| 52 | // -- input variables
|
|---|
| 53 | Real Vdin(start = 120);
|
|---|
| 54 | Real Vdout(start = 120);
|
|---|
| 55 | // -- output variables, scaled
|
|---|
| 56 | output Real _Vd, _h;
|
|---|
| 57 | // Initializating in steady state
|
|---|
| 58 |
|
|---|
| 59 | initial equation
|
|---|
| 60 | der(h[1:end-1]) = zeros(NVd);
|
|---|
| 61 | der(Vd[:]) = zeros(NVd);
|
|---|
| 62 |
|
|---|
| 63 | // Equations constituting the model
|
|---|
| 64 | equation
|
|---|
| 65 | // Input values
|
|---|
| 66 | //Vdin = 120;
|
|---|
| 67 | Vdout = 120;
|
|---|
| 68 |
|
|---|
| 69 | if time < 1e3 then
|
|---|
| 70 | Vdin = 120;
|
|---|
| 71 | elseif time < 1.2e3 then
|
|---|
| 72 | Vdin = 145;
|
|---|
| 73 | else
|
|---|
| 74 | Vdin = 120;
|
|---|
| 75 | end if;
|
|---|
| 76 |
|
|---|
| 77 | // Defining auxiliary variables
|
|---|
| 78 | A[:] = h[:]*w;
|
|---|
| 79 | per[:] = w*oneh[:] + 2*h[:];
|
|---|
| 80 | //
|
|---|
| 81 | h_[:] = (h[1:end-1] + h[2:end])/2;
|
|---|
| 82 | A_[:] = h_[:]*w;
|
|---|
| 83 | per_[:] = (per[1:end-1] + per[2:end])/2;
|
|---|
| 84 | R_[:] = A_[:]./per_[:];
|
|---|
| 85 | C_[:] = kS*((R_[:]).^(1/6));
|
|---|
| 86 | //
|
|---|
| 87 | Md_rho_i[1] = Vdin^2/A[1];
|
|---|
| 88 | for n in 2:NVd-1 loop
|
|---|
| 89 | vMdip[n-1] = abs(Vd[n-1])*max(Vd[n-1],0)/A_[n-1];
|
|---|
| 90 | vMdim[n-1] = abs(Vd[n+1])*max(-Vd[n+1],0)/A_[n+1];
|
|---|
| 91 | Md_rho_i[n] = vMdip[n-1] + vMdim[n-1];
|
|---|
| 92 | end for;
|
|---|
| 93 | Md_rho_i[end] = abs(Vd[end-1])*max(Vd[end-1],0)/A_[end-1];
|
|---|
| 94 | //
|
|---|
| 95 | for n in 1:NVd-1 loop
|
|---|
| 96 | Md_rho_o[n] = Vd[n]^2/A_[n];
|
|---|
| 97 | end for;
|
|---|
| 98 | Md_rho_o[NVd] = Vdout^2/A[NVd+1];
|
|---|
| 99 | //
|
|---|
| 100 | // vMd[:] = (Md_rho_i[:] - Md_rho_o[:])/dx;
|
|---|
| 101 | // vp[:] = g*w*cos(th)*(h[1:end-1].^2 - h[2:end].^2)/(2*dx);
|
|---|
| 102 | // vg[:] = A_[:]*g*sin(th);
|
|---|
| 103 | // vf[:] = - g*per_[:].*abs(Vd[:]).*Vd[:]./(C_[:].*A_[:]).^2;
|
|---|
| 104 | // Differential equations
|
|---|
| 105 | der(h[1]) = (Vdin-Vd[1])/(w*dx/2);
|
|---|
| 106 | der(h[2:NVd]) = (Vd[1:end-1] - Vd[2:end])/(w*dx);
|
|---|
| 107 | der(h[NVd+1]) = (Vd[NVd] - Vdout)/(w*dx/2);
|
|---|
| 108 | //
|
|---|
| 109 | der(Vd[:]) = (Md_rho_i[:] - Md_rho_o[:])/dx
|
|---|
| 110 | + g*w*cos(th)*(h[1:end-1].^2 - h[2:end].^2)/(2*dx)
|
|---|
| 111 | + A_[:]*g*sin(th)
|
|---|
| 112 | - g*per_[:].*abs(Vd[:]).*Vd[:]./(C_[:].*A_[:]).^2;
|
|---|
| 113 | // Outputs
|
|---|
| 114 | _Vd = Vd[end];
|
|---|
| 115 | _h = h[end];
|
|---|
| 116 | end simShallowRiver;
|
|---|
| 117 | //
|
|---|
| 118 | model simShallowRiverWorks
|
|---|
| 119 | // Main Shallow River model
|
|---|
| 120 | // author: Bernt Lie
|
|---|
| 121 | // Telemark University College
|
|---|
| 122 | // September 10, 2013
|
|---|
| 123 | //
|
|---|
| 124 | // Constants
|
|---|
| 125 | constant Real g = 9.81 "Gravity, m/s2";
|
|---|
| 126 | // Parameters
|
|---|
| 127 | parameter Real w = 100 "River width, m";
|
|---|
| 128 | parameter Real L = 5e3 "River length, m";
|
|---|
| 129 | parameter Real H = 57 "River bed drop, m";
|
|---|
| 130 | parameter Real th = asin(H/L) "River bed angle, rad";
|
|---|
| 131 | parameter Real rho = 1e3 "Density of water, kg/m3";
|
|---|
| 132 | parameter Real kS = 20 "Strickler's friction factor, m0.33/s";
|
|---|
| 133 | parameter Integer NVd = 18 "Number of momentum balance segments, -";
|
|---|
| 134 | parameter Real dx = L/NVd "discretization step, m";
|
|---|
| 135 | parameter Real oneh[NVd+1] = ones(NVd+1);
|
|---|
| 136 | // Initial state parameters
|
|---|
| 137 | parameter Real h0 = 4;// 0.5275 "Initial guess river level, m";
|
|---|
| 138 | parameter Real Vd0 = 120 "Initial guess volumetric flow rate, m3/s";
|
|---|
| 139 | // Declaring variables
|
|---|
| 140 | // -- states
|
|---|
| 141 | Real h[NVd+1](each start = h0); //, each fixed = true) "Level states, m";
|
|---|
| 142 | Real Vd[NVd](each start = Vd0); //, each fixed = true) "Volumetric flow rates, m3/s";
|
|---|
| 143 | // -- auxiliary variables at mass knots
|
|---|
| 144 | Real A[NVd+1] "Area perpendicular to flow direction, m2";
|
|---|
| 145 | Real per[NVd+1] "Wetting perimeter, m";
|
|---|
| 146 | // -- auxiliary variables at momentum knots
|
|---|
| 147 | Real h_[NVd] "Staggered levels, m";
|
|---|
| 148 | Real A_[NVd] "Staggered areas, m2";
|
|---|
| 149 | Real Md_rho_i[NVd] "Input momentum flow/density, m4/s2";
|
|---|
| 150 | Real Md_rho_o[NVd] "Output momentum flow/density, m4/s2";
|
|---|
| 151 | Real per_[NVd] "Staggered wetted perimeters, m";
|
|---|
| 152 | Real R_[NVd] "Staggered hydraulic radii, m";
|
|---|
| 153 | Real C_[NVd] "Staggered Chezy coefficient, ...";
|
|---|
| 154 | Real vMd[NVd] "stupid vector";
|
|---|
| 155 | Real vp[NVd] "stupid vector";
|
|---|
| 156 | Real vg[NVd] "stupid vector";
|
|---|
| 157 | Real vf[NVd] "stupid vector";
|
|---|
| 158 | Real vMdip[NVd-2] "stupid vector";
|
|---|
| 159 | Real vMdim[NVd-2] "stupid vector";
|
|---|
| 160 | // -- input variables
|
|---|
| 161 | Real Vdin(start = 120);
|
|---|
| 162 | Real Vdout(start = 120);
|
|---|
| 163 | // -- output variables, scaled
|
|---|
| 164 | output Real _Vd, _h;
|
|---|
| 165 | // Initializating in steady state
|
|---|
| 166 |
|
|---|
| 167 | initial equation
|
|---|
| 168 | der(h[1:end-1]) = zeros(NVd);
|
|---|
| 169 | der(Vd[:]) = zeros(NVd);
|
|---|
| 170 |
|
|---|
| 171 | // Equations constituting the model
|
|---|
| 172 | equation
|
|---|
| 173 | // Input values
|
|---|
| 174 | //Vdin = 120;
|
|---|
| 175 | Vdout = 120;
|
|---|
| 176 |
|
|---|
| 177 | if time < 1e3 then
|
|---|
| 178 | Vdin = 120;
|
|---|
| 179 | elseif time < 1.2e3 then
|
|---|
| 180 | Vdin = 145;
|
|---|
| 181 | else
|
|---|
| 182 | Vdin = 120;
|
|---|
| 183 | end if;
|
|---|
| 184 |
|
|---|
| 185 | // Defining auxiliary variables
|
|---|
| 186 | A[:] = h[:]*w;
|
|---|
| 187 | per[:] = w*oneh[:] + 2*h[:];
|
|---|
| 188 | //
|
|---|
| 189 | h_[:] = (h[1:end-1] + h[2:end])/2;
|
|---|
| 190 | A_[:] = h_[:]*w;
|
|---|
| 191 | per_[:] = (per[1:end-1] + per[2:end])/2;
|
|---|
| 192 | R_[:] = A_[:]./per_[:];
|
|---|
| 193 | C_[:] = kS*((R_[:]).^(1/6));
|
|---|
| 194 | //
|
|---|
| 195 | Md_rho_i[1] = Vdin^2/A[1];
|
|---|
| 196 | for n in 2:NVd-1 loop
|
|---|
| 197 | vMdip[n-1] = abs(Vd[n-1])*max(Vd[n-1],0)/A_[n-1];
|
|---|
| 198 | vMdim[n-1] = abs(Vd[n+1])*max(-Vd[n+1],0)/A_[n+1];
|
|---|
| 199 | Md_rho_i[n] = vMdip[n-1] + vMdim[n-1];
|
|---|
| 200 | end for;
|
|---|
| 201 | Md_rho_i[end] = abs(Vd[end-1])*max(Vd[end-1],0)/A_[end-1];
|
|---|
| 202 | //
|
|---|
| 203 | for n in 1:NVd-1 loop
|
|---|
| 204 | Md_rho_o[n] = Vd[n]^2/A_[n];
|
|---|
| 205 | end for;
|
|---|
| 206 | Md_rho_o[NVd] = Vdout^2/A[NVd+1];
|
|---|
| 207 | //
|
|---|
| 208 | vMd[:] = (Md_rho_i[:] - Md_rho_o[:])/dx;
|
|---|
| 209 | vp[:] = g*w*cos(th)*(h[1:end-1].^2 - h[2:end].^2)/(2*dx);
|
|---|
| 210 | vg[:] = A_[:]*g*sin(th);
|
|---|
| 211 | vf[:] = - g*per_[:].*abs(Vd[:]).*Vd[:]./(C_[:].*A_[:]).^2;
|
|---|
| 212 | // Differential equations
|
|---|
| 213 | der(h[1]) = (Vdin-Vd[1])/(w*dx/2);
|
|---|
| 214 | der(h[2:NVd]) = (Vd[1:end-1] - Vd[2:end])/(w*dx);
|
|---|
| 215 | der(h[NVd+1]) = (Vd[NVd] - Vdout)/(w*dx/2);
|
|---|
| 216 | //
|
|---|
| 217 | der(Vd[:]) = vMd[:] + vp[:] + vg[:] + vf[:];
|
|---|
| 218 | // Outputs
|
|---|
| 219 | _Vd = Vd[end];
|
|---|
| 220 | _h = h[end];
|
|---|
| 221 | end simShallowRiverWorks;
|
|---|
| 222 | // End package
|
|---|
| 223 | end myShallowRiver;
|
|---|
| 224 |
|
|---|