Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

The phase density function is usually denoted as $f(\mathbf{x},\mathbf{v},t)$ which gives probable number of particles moving with velocity $ \mathbf{v}$ at position $\mathbf{x}$ at time t. Also we assume that position and velocities of particles are not correlated i.e. $\mathbf{x} $ and $\mathbf{v}$ are independent.

We use $f(\mathbf{x},\mathbf{v},t)$ as a basis Lattice Boltzmann functionto solve fluid dynamics equations. $$ f_i(\mathbf {x} +\Delta \mathbf {x}, t + \Delta t) - f_i(\mathbf {x}, t ) = -\frac{\Delta t}{\tau} (f_i - f^{eq}_i) $$

The entire point of solving fluid dynamics equation is(If I am correct) to know velocity at a given point and time. How can we use $f(\mathbf{x},\mathbf{v},t)$ to proceed with lattice Boltzmann equation when $f(\mathbf{x},\mathbf{v},t)$ has multiple values of velocities at given point $\mathbf{x}$ ?

share|improve this question
add comment

1 Answer 1

At a given point in space, there are several values of $f_i$, one for each discrete velocity $v_i$. So you have to apply the lattice-Boltzmann equation as many times. This is exactly the point of the lattice-Boltzmann method: each "element" is actually defined by its discrete value of the velocity. You apply the equation for each of these elements which have a given, fixed velocity.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.