Hi, everyone,

I have a small but important question. In the Navier-Stokes equations, there exist a dependent variable, "p" (pressure), and some books call this "static pressure", then my question arise. For example, in the jet DNS, the environment pressure is 1atm(101325Pa), then in the code, how to set the value "p", 0 or 101325Pa. In fact, what I mean is what "static pressure" means? Thanks a lot for this. If you can recommend some paper focusing on this, I will be further grateful.

The term static pressure comes from fluid statics (study of fluids at rest, or more correctly, fluids which are not in acceleration) where the pressure is uniform and isotropic. In hydodynamics, if you are moving with the local fluid velocity and measure the pressure field then you can separate it out into an isotropic part and a part which depends on direction. The isotropic part is called static pressure, static because you measure it in a frame in which the fluid is locally at rest. In practice you can measure static pressure using a manometer whose mouth is kept parallel to the streamlines. In a pitot tube the holes on the sides of the tube sense static pressure provided of course that the tube is kept parallel to the oncoming stream.

Thanks for your kind reply, Praveen. Then I know that in the simulation, the value "101325Pa" should be used in my case mentioned above. However, in the normalized equations, the reference value for pressure "p", p_r, is usually set to rho_r*u_r^2, if I take the air as the computing gas, then rho_r=1.2kg/m^3, u_r=10-20m/s (ordinary conditions in jet experiments and simulations), so p_r=rho_r*u_r^2=1.2*[100, 400]=[1200, 4800], i.e. 1200<p_r<4800. The normalized pressure, p*, used at the initial computation will be p*=p/p_r=101325/ [1200, 4800]=[21, 85]. In the normalized rho, u, v and w equations, the approximate dimensions are 1, 1, 0 and 0, repectively. But the approximate dimension for p equation is [21, 85]. The differences between the equations are extremely large so that it's very difficult to carry out the computation. In fact, I cannot handle such a simulation case mentioned above which is really common. I can only raise the u_r value to 100, for example, to avoid this. How do any others deal with such situation? Thanks a lot for this. I should mention earlier that: (1) the compressible equation set has been used in my DNS; (2) the dependent variables of every equation are rho, u, v, p in the two-dimensional simulation.

<continuing page> ... so p_r=rho_r*u_r^2=1.2*[100, 400]=[1200, 4800], i.e. 1200<p_r<4800. The normalized pressure, p*, used at the initial computation will be p*=p/p_r=101325/[1200, 4800]=[21, 85]. In the normalized rho, u, v and w equations, the approximate dimensions are 1, 1, 0 and 0, repectively. But the approximate dimension for p equation is [21, 85]. The differences between the equations are extremely large so that it's very difficult to carry out the computation. In fact, I cannot handle such a simulation case mentioned above which is really common. I can only raise the u_r value to 100, for example, to avoid this. How do any others deal with such situation? Thanks a lot for this. I should mention earlier that: (1) the compressible equation set has been used in my DNS; (2) the dependent variables of every equation are rho, u, v, p in the two-dimensional simulation.

Thanks for your kind reply, Praveen. Then I know that in the simulation, the value "101325Pa" should be used in my case mentioned above. However, in the normalized equations, the reference value for pressure "p", p_r, is usually set to rho_r*u_r^2, if I take the air as the computing gas, then rho_r=1.2kg/m^3, u_r=10-20m/s (ordinary conditions in jet experiments and simulations), so p_r=rho_r*u_r^2=1.2*[100, 400]=[1200, 4800]. The normalized pressure, p*, used at the initial computation will be p*=p/p_r=101325/[1200, 4800]=[21, 85]. In the normalized rho, u, v and w equations, the approximate dimensions are 1, 1, 0 and 0, repectively. But the approximate dimension for p equation is [21, 85]. The differences between the equations are extremely large so that it's very difficult to carry out the computation. In fact, I cannot handle such a simulation case mentioned above which is really common. I can only raise the u_r value to 100, for example, to avoid this. How do any others deal with such situation? Thanks a lot for this. I should mention earlier that: (1) the compressible equation set has been used in my DNS; (2) the dependent variables of every equation are rho, u, v, p in the two-dimensional simulation.