Circular dam break problem

Hi there,

I’m still relatively new to the LB Method. I am investigating the problem of dam breaks and i have managed to simulate a 2d dam break case where the initial conditions for the height, rho, are as follows…

rho = (rho_l+rho_r)/2ones(M,N)-z;
rho = 10
ones(M,N);
rho(find(x<10))=5;

I am now trying to create a circular dam break problem so the initial state of the fluid is effectively a cyclindrical shape in the middle of a 50x50 grid. Can anybody tell me the best way to approach this for setting the initial state? I was thinking of something as shown below, where a circular area is selected, and the rho is set to 10 in this area, otherwise it is 1. Is this a good place to start? Any help would be great. Thanks.

rho = 1*ones(M,N);
rho(find(15<x^x+y^y<35))=10;

Hi,

You are simulating water, which means, an incompressible fluid, right? In this case, a density ratio of 10 inside the fluid is physically not meaningful (and it is probably numerically unstable, right?). In an incompressible regime, density variations are used to represent pressure fluctuations around the reference pressure (usually rho=1). Even in extreme cases like a dam break, the density must always be somewhere close to 1. If it’s not, your simulation runs in a compressible regime and does not find solutions to the incompressbile Navier-Stokes equations any more. To give you an idea, you might want to try rho=1.01 inside the circular area, or something alike. At some point, you’ll need to quantify the physics you want to represent, and calculate the unit conversions (search for unit conversion in this forum). Thus, you’ll need to know the physical value of the pressure inside the cylinder and apply unit conversions to calculate the density in the simulation.