%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This file is part of NS2DDV.                                                      %
%                                                                                   %
% Copyright(C) 2011-2018    C. Calgaro  (caterina.calgaro@math.univ-lille1.fr)      %
%                           E. Creusé   (emmanuel.creuse@math.univ-lille1.fr)       %
%                           T. Goudon   (thierry.goudon@inria.fr)                   %
%                           A. Mouton   (alexandre.mouton@math.univ-lille1.fr)      %
%                                                                                   %
% NS2DDV is free software: you can redistribute it and/or modify it under the terms %
% of the GNU General Public License as published by the Free Software Foundation,   %
% either version 3 of the License, or (at your option) any later version.           %
%                                                                                   %
% NS2DDV is distributed in the hope that it will be useful, but WITHOUT ANY         %
% WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A   %
% PARTICULAR PURPOSE. See the GNU General Public License for more details.          %
%                                                                                   %
% You should have received a copy of the GNU General Public License along with      %
% NS2DDV. If not, see <http://www.gnu.org/licenses/>.                               %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function[p,u,rho] = exact_solution_nsdv(x, y, time, PARAMETERS)

	% INPUT
	% x					x-coordinate of the point at which the exact solution has to be evaluated
	% y					y-coordinate of the point at which the exact solution has to be evaluated
	% time				Time value
	% PARAMETERS		List of simulation parameters
	%
	% OUTPUT
	% p					Exact pressure
	% u					Exact velocity
	% rho				Exact density

	switch PARAMETERS.TESTCASE
		case {'RTIN', 'CAEN', 'DROP'}
			% No analytical solution : we answer 0
			p = 0.;
			u = zeros(1,2);
			rho = 0.;

		case {'EXAC'}
			u = zeros(1,2);
			u(:,1) = -y*cos(time);
			u(:,2) = x*cos(time);
			rho = 2. + cos(sin(time))*x + sin(sin(time))*y;
			switch PARAMETERS.DOMAIN.GEOMETRY
				case {'RECTANGLE'}
					Lx = PARAMETERS.DOMAIN.XMAX-PARAMETERS.DOMAIN.XMIN;
					Ly = PARAMETERS.DOMAIN.YMAX-PARAMETERS.DOMAIN.YMIN;
					xx = 2*pi*(x-PARAMETERS.FE.NFX_X)/Lx;
					yy = 2*pi*(y-PARAMETERS.FE.NFX_Y)/Ly;
					p = sin(time) * sin(xx) * sin(yy);
				case {'CIRCLE', 'DIHEDRON', 'FROM_FILE'}
					error(sprintf('EXAC test case is only compatible with RECTANGLE domain geometry\n'));
				otherwise
					error(sprintf('Unknown domain geometry\n'));
			end

		case {'EXACNEU'}
			switch PARAMETERS.DOMAIN.GEOMETRY
				case {'RECTANGLE'}
					Lx = PARAMETERS.DOMAIN.XMAX-PARAMETERS.DOMAIN.XMIN;
					Ly = PARAMETERS.DOMAIN.YMAX-PARAMETERS.DOMAIN.YMIN;
					xx = (x-PARAMETERS.DOMAIN.XMIN)/Lx;
					yy = (y-PARAMETERS.DOMAIN.YMIN)/Ly;
					u = zeros(1,2);
					u(:,1) = sin(xx) * sin(yy+time);
					u(:,2) = cos(xx) * cos(yy+time);
					p = (1./(PARAMETERS.PHYSICAL.RE*Lx)) * cos(xx) * sin(yy+time);
					rho = 1.;

		otherwise
			error(sprintf('Unknown test case.\n'));
	end

end