TS transient variables
Suppose c(p)
is an equation of state writing conservative variables in terms of primitive variables. A transient system may express the time derivative of the conserved variables via a chain rule
F(p, p_t) := c_p p_t - f(p) = 0
but this formulation is typically not conservative. (One way to understand the lack of conservation is that RK and multistep methods typically approximate the trajectory p(t)
as a polynomial, in which case c(t)
is not a polynomial. We propose adding an interface to define c(p)
such that the user may implement
G(p, c_t) := c_t - f(p)
to obtain a conservative integrator. This is possible with BDF and related methods, but I'm not aware of a clean way to do this for Runge-Kutta.