Utilities for the Fluid Properties Module

1D solver

The 1D Newton method solver is used to solve the problem:

• Find $z$ such that $f(x, z) = y$, with $x$, $y$ known constants and $f$ a function.

$f$ should compute both its return value and the derivatives of its value with regards to both its variables using references.

The routine will error if a NaN is encountered or if the maximum number of iterations is exceeded.

2D solver

The 2D Newton method solver is used to solve the problem:

$$\begin{split} f1(x, y) &= a \\ f2(x, y) &= b \end{split}$$

with $a$, $b$ known constants, $f1$, $f2$ functions and $x$, $y$ the real-valued variables to solve for.

The functions should compute both their return value and the derivatives of their value with regards to both variables using references.

The routine will not error if a NaN is encountered or if the maximum number of iterations is exceeded. Instead, a converged boolean will be set to false, and the routine will return the last valid estimates of $x$ and $y$. It is the responsibility of the user to handle this unconverged output.