Basically, for solving 1D flow equations, one uses the mass, momentum and energy equations (Also known as Euler equations). Say now I have $N$ elements in series, will I be using $3N$ equations?
|comments disabled on deleted / locked posts|
migrated from stackoverflow.com Jul 29 at 16:19
This question came from our site for professional and enthusiast programmers.
closed as unclear what you're asking by BebopButUnsteady, AlanSE, Dilaton, Qmechanic♦ Jul 29 at 20:16
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking.If this question can be reworded to fit the rules in the help center, please edit the question.
Not exactly. You still have your three Euler equations: $$ \partial_t\rho + \partial_x\rho v_x=0 $$ $$ \partial_t\left(\rho v_x\right)+\partial_x\left(\rho v_x^2+P\right)=0 $$ $$ \partial_te +\partial_x\left[\left(e+P\right)v_x\right]=0 $$ but what you are doing is solving the system of 3 equations $N$ times (once for each cell).
It will be worth your while to read these lecture notes on partial differential equations from Arizona State University.