ControlPoints.m

%% Generate control points for the spline reconstruction of the fluid EoS
%% Ideal Gas equation in vapor state
%% Tait Equation in liquid state
%% Saikat Mukherjee Purdue University September 27 2022

clear all;
close all;

R      = 461.5;
K0     = 2.15*10^9;
n      = 7.15;
P0     = 101325;
rho0   = 1000;
theta  = 300;
rho_l  = 996.5;
rho_v  = 0.0256;
DeltaP = 10000.0;

%% Control Point 1 : Ideal Gas Equation
rho1 = rho_v;
p1   = rho_v*R*theta;

%% Control Point 6 : Tait EoS
rho6 = rho_l;
p6   = K0/n*( (rho_l/rho0)^n-1 ) + P0;

%% Control Point 2 : Match the slope from the ideal gas equation
rho2 = rho1 + DeltaP/(R*theta);
p2   = p1 + DeltaP;

%% Control Point 5 : Match the slope from Tait EoS
rho5 = rho6 - DeltaP/(K0/rho0^n*rho_l^(n-1));
p5   = p6 - DeltaP;

%% Control Point 3
rho3 = 0.25*(rho_l+3*rho_v);
p3   = p2;

%% Control Point 4
rho4 = 0.25*(rho_v+3*rho_l);
p4   = p5;

t = [0 0 0 1 2 3 4 4 4];
bspline(t)

% x = [ rho1 rho2 rho3 rho4 rho5 rho6 ];
% y = [ p1 p2 p3 p4 p5 p6 ];
% xx = rho1:0.01:rho6;
% yy = spline(x,y,xx);
% plot(x,y,'o',xx,yy);