mathematicsoftsunamis-source.nb

simulate Tsunamis using mathematica

          
          Subscript[$CellContext`\[Lambda], $CellContext`min], 
          Subscript[$CellContext`\[Lambda], $CellContext`max]}, PlotRange -> 
         All, PlotPoints -> $CellContext`nxy, Mesh -> None, MaxRecursion -> 1,
          ContourShading -> None, ContourStyle -> Opacity[0.15], 
         Contours -> {-3500, -3000, -2500, -2000, -1500, -1000, -500}]; \
$CellContext`swe = {D[
            $CellContext`h[$CellContext`\[Lambda], $CellContext`\[Phi], \
$CellContext`t], $CellContext`t] + (
            D[$CellContext`u[$CellContext`\[Lambda], $CellContext`\[Phi], \
$CellContext`t] ($CellContext`h[$CellContext`\[Lambda], $CellContext`\[Phi], \
$CellContext`t] - $CellContext`b[$CellContext`\[Lambda], \
$CellContext`\[Phi]]), $CellContext`\[Lambda]] + 
            D[($CellContext`v[$CellContext`\[Lambda], $CellContext`\[Phi], \
$CellContext`t] ($CellContext`h[$CellContext`\[Lambda], $CellContext`\[Phi], \
$CellContext`t] - $CellContext`b[$CellContext`\[Lambda], \
$CellContext`\[Phi]])) 
              Cos[$CellContext`\[Phi]], $CellContext`\[Phi]])/($CellContext`R 
           Cos[$CellContext`\[Phi]]) == 0, D[
             $CellContext`u[$CellContext`\[Lambda], $CellContext`\[Phi], \
$CellContext`t], $CellContext`\[Phi]] ($CellContext`v[$CellContext`\[Lambda], \
$CellContext`\[Phi], $CellContext`t]/$CellContext`R) + $CellContext`g (D[
              $CellContext`h[$CellContext`\[Lambda], $CellContext`\[Phi], \
$CellContext`t], $CellContext`\[Lambda]]/($CellContext`R 
            Cos[$CellContext`\[Phi]])) + D[
            $CellContext`u[$CellContext`\[Lambda], $CellContext`\[Phi], \
$CellContext`t], $CellContext`t] + $CellContext`u[$CellContext`\[Lambda], \
$CellContext`\[Phi], $CellContext`t] (D[
              $CellContext`u[$CellContext`\[Lambda], $CellContext`\[Phi], \
$CellContext`t], $CellContext`\[Lambda]]/($CellContext`R 
            Cos[$CellContext`\[Phi]])) == $CellContext`f \
$CellContext`v[$CellContext`\[Lambda], $CellContext`\[Phi], $CellContext`t], 
         D[
             $CellContext`v[$CellContext`\[Lambda], $CellContext`\[Phi], \
$CellContext`t], $CellContext`\[Phi]] ($CellContext`v[$CellContext`\[Lambda], \
$CellContext`\[Phi], $CellContext`t]/$CellContext`R) + $CellContext`g (D[
              $CellContext`h[$CellContext`\[Lambda], $CellContext`\[Phi], \
$CellContext`t], $CellContext`\[Phi]]/$CellContext`R) + D[
            $CellContext`v[$CellContext`\[Lambda], $CellContext`\[Phi], \
$CellContext`t], $CellContext`t] + $CellContext`u[$CellContext`\[Lambda], \
$CellContext`\[Phi], $CellContext`t] (D[
              $CellContext`v[$CellContext`\[Lambda], $CellContext`\[Phi], \
$CellContext`t], $CellContext`\[Lambda]]/($CellContext`R 
            Cos[$CellContext`\[Phi]])) == (-$CellContext`f) \
$CellContext`u[$CellContext`\[Lambda], $CellContext`\[Phi], $CellContext`t]}; 
      Block[{$CellContext`R = 6378000, $CellContext`\[Omega] = 
         2 (Pi/(24 3600)), $CellContext`f = (2 $CellContext`\[Omega]) 
          Sin[$CellContext`\[Phi]], $CellContext`g = 9.8, $CellContext`s = 
         0.95}, $CellContext`sol = First[
          ReplaceAll[$CellContext`h, 
           
           NDSolve[{$CellContext`swe, $CellContext`h[$CellContext`\[Lambda], \
$CellContext`\[Phi], 0] == E^((-2000) $CellContext`ldist[{
                   Subscript[$CellContext`\[Lambda], $CellContext`e], 
                   Subscript[$CellContext`\[Phi], 1]}, {
                   Subscript[$CellContext`\[Lambda], $CellContext`e], 
                   
                   Subscript[$CellContext`\[Phi], 
                    2]}][{$CellContext`\[Lambda], $CellContext`\[Phi]}]^2), \
$CellContext`u[$CellContext`\[Lambda], $CellContext`\[Phi], 0] == 
             0, $CellContext`v[$CellContext`\[Lambda], $CellContext`\[Phi], 
               0] == 0, $CellContext`h[$CellContext`\[Lambda], 
               
               Subscript[$CellContext`\[Phi], $CellContext`min], \
$CellContext`t] == $CellContext`h[$CellContext`\[Lambda], 
               
               Subscript[$CellContext`\[Phi], $CellContext`max], \
$CellContext`t], $CellContext`h[
               
               Subscript[$CellContext`\[Lambda], $CellContext`min], \
$CellContext`\[Phi], $CellContext`t] == $CellContext`h[
               
               Subscript[$CellContext`\[Lambda], $CellContext`max], \
$CellContext`\[Phi], $CellContext`t]}, $CellContext`h, \
{$CellContext`\[Lambda], 
             Subscript[$CellContext`\[Lambda], $CellContext`min], 
             
             Subscript[$CellContext`\[Lambda], $CellContext`max]}, \
{$CellContext`\[Phi], 
             Subscript[$CellContext`\[Phi], $CellContext`min], 
             
             Subscript[$CellContext`\[Phi], $CellContext`max]}, \
{$CellContext`t, 0, $CellContext`T}, 
            DependentVariables -> {$CellContext`h, $CellContext`u, \
$CellContext`v}, 
            Method -> {
             "MethodOfLines", 
              "SpatialDiscretization" -> {
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                "MinPoints" -> {$CellContext`nxy, $CellContext`nxy}, 
                "MaxPoints" -> {$CellContext`nxy, $CellContext`nxy}, 
                "DifferenceOrder" -> "Pseudospectral"}}]]]]; Null); 
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