Estimate time step at each node
[Mobj] = function estimate_ts(Mobj)
DESCRIPTION:
Calculate barotropic time step
INPUT
Mobj = matlab mesh object
u = anticipated maximum current speed
zeta = anticipated maximum surface elevation
OUTPUT:
Mobj = matlab structure containing mesh time step
EXAMPLE USAGE
Mobj = estimate_ts(Mobj)
Author(s):
Geoff Cowles (University of Massachusetts Dartmouth)
Pierre Cazenave (Plymouth Marine Laboratory)
Revision history
2012-07-14 Add great circle approximation if only provided with
latitude and longitudes. Also add arguments to the function to define
current velocity and tidal amplitudes.
2016-02018 Update the help to reflect the required variables.
2017-09-01 Tidy the code a bit.
==============================================================================0001 function [Mobj] = estimate_ts(Mobj,u,zeta) 0002 0003 % Estimate time step at each node 0004 % 0005 % [Mobj] = function estimate_ts(Mobj) 0006 % 0007 % DESCRIPTION: 0008 % Calculate barotropic time step 0009 % 0010 % INPUT 0011 % Mobj = matlab mesh object 0012 % u = anticipated maximum current speed 0013 % zeta = anticipated maximum surface elevation 0014 % 0015 % OUTPUT: 0016 % Mobj = matlab structure containing mesh time step 0017 % 0018 % EXAMPLE USAGE 0019 % Mobj = estimate_ts(Mobj) 0020 % 0021 % Author(s): 0022 % Geoff Cowles (University of Massachusetts Dartmouth) 0023 % Pierre Cazenave (Plymouth Marine Laboratory) 0024 % 0025 % Revision history 0026 % 2012-07-14 Add great circle approximation if only provided with 0027 % latitude and longitudes. Also add arguments to the function to define 0028 % current velocity and tidal amplitudes. 0029 % 2016-02018 Update the help to reflect the required variables. 0030 % 2017-09-01 Tidy the code a bit. 0031 % 0032 %============================================================================== 0033 0034 [~, subname] = fileparts(mfilename('fullpath')); 0035 global ftbverbose 0036 if ftbverbose 0037 fprintf('\nbegin : %s\n', subname) 0038 end 0039 0040 %------------------------------------------------------------------------------ 0041 % Set constants 0042 %------------------------------------------------------------------------------ 0043 0044 g = 9.81; % gravitational acceleration 0045 0046 if(~Mobj.have_bath) 0047 error('can''t estimate the time step without bathymetry') 0048 end 0049 0050 %------------------------------------------------------------------------------ 0051 % Compute the time step estimate 0052 %------------------------------------------------------------------------------ 0053 if Mobj.have_xy 0054 x = Mobj.x; 0055 y = Mobj.y; 0056 else 0057 % Will convert to metres when calculating element edge length 0058 x = Mobj.lon; 0059 y = Mobj.lat; 0060 end 0061 h = max(Mobj.h,0); 0062 tri = Mobj.tri; 0063 nVerts = Mobj.nVerts; 0064 nElems = Mobj.nElems; 0065 0066 ts = inf(nVerts,1); 0067 lside = zeros(nVerts,1); 0068 for i=1:nElems 0069 n1 = tri(i,1); 0070 n2 = tri(i,2); 0071 n3 = tri(i,3); 0072 nds = [n1 n2 n3]; 0073 % Check whether we have x and y values and use great circle 0074 % approximations if we don't. 0075 if Mobj.have_xy 0076 lside(i) = sqrt((x(n1)-x(n2))^2 + (y(n1)-y(n2))^2); 0077 else 0078 lside(i) = haversine(x(n1),y(n1),x(n2),y(n2)); 0079 end 0080 dpth = max(h(nds))+zeta; 0081 dpth = max(dpth,1); 0082 ts(nds) = min(ts(nds),lside(i)/(sqrt(g*dpth) + u)); 0083 end 0084 if ftbverbose 0085 fprintf('minimum time step: %f seconds\n',min(ts)); 0086 end 0087 Mobj.ts = ts; 0088 Mobj.have_ts = true; 0089 Mobj.lside=lside; 0090 if ftbverbose 0091 fprintf('end : %s\n', subname) 0092 end 0093 0094 function km=haversine(lat1,lon1,lat2,lon2) 0095 % Haversine function to calculate first order distance measurement. Assumes 0096 % spherical Earth surface. Lifted from: 0097 % 0098 % http://www.mathworks.com/matlabcentral/fileexchange/27785 0099 % 0100 R = 6371000; % Earth's mean radius in metres 0101 delta_lat = lat2 - lat1; % difference in latitude 0102 delta_lon = lon2 - lon1; % difference in longitude 0103 a = sin(delta_lat/2)^2 + cos(lat1) * cos(lat2) * ... 0104 sin(delta_lon/2)^2; 0105 c = 2 * atan2(sqrt(a), sqrt(1-a)); 0106 km = R * c; % distance in metres 0107