hi everyone, I'm solving cavitating flow model by 1-D isothermal euler equation, solved by approximate Roe solver. i have velocity value at 1 boundary, how can i find the corresponding pressure? can i assume p_boundary = p(1), where p(1) is the node next to the boundary? some papers solved this by compatibility relation? how do i implement it?

2) if i change the density to pressure as the variable in the equation, i obtain pressure checker board pattern in the solution. why is this so? i solved this by Roe's solver also.

Many thanks for your help!

well, I think better way always use nondimensionalised form. The following equations will help then.

e_vol= {1 / (M*M*gamma*(gamma-1)}+ 1/2 h= {1 / (M*M*(gamma-1)}+ 1/2 pr= (gamma-1)* (e_vol - 0.5) Vx= c * M * cosA Vy= c* M * sinA

use a combination of above eqns and u can get it.

hi,Tushar many thanks for your suggestion. I'm not familiar with the notation you used, could you explain it to me? or could you suggest a reference to me that derives these relationship? the fluid medium in my model is water / liquid + air, are these relationship also applicable? because from my understanding, gamma term (cv/cp) is only applicable to gas dynamics, am I right? Thanks again!