AbstractIn this paper, we consider a version of energy minimisation technique applied to images of a 2D fluid flow. The two Navier–Stokes equations describe the static flow of a 2D fluid in terms of velocity field, (u, v), pressure field, p and forcing field, f. Apart from these two Navier–Stokes equations, we have the incompressibility condition to evaluate the three parameters. While implementing this system, random noise (usually non-Gaussian) creeps into the random force field $$\underline{f}(x,y)$$
f
̲
(
x
,
y
)
. We denote this random field by $$\delta \underline{f}(x,y)$$
δ
f
̲
(
x
,
y
)
having zero mean and non-trivial second and third moments. We assume that these two moments are known except for some unknown parameters $$\underline{\theta }$$
θ
̲
(like mean, variance, co-variance, skewness, etc.) which we wish to estimate. In the proposed technique, we first calculate the approximate shift in the average fluid energy defined as a quadratic function of the velocity field. The energy method then requires that $$\underline{\theta }$$
θ
̲
should be such that this average increases in the energy due to the random forcing component be minimised. We should, however, note that the standard statistical approach to force field estimation is to calculate the velocity field as a function of the force field and then adopt the statistical moment matching technique. Such an approach assumes spatial ergodicity of the velocity field. This approach to force field estimation is more accurate from the statistical moment matching view point but works only if velocity measurements are made. The former technique of energy minimisation does not require any velocity measurements. Both of these techniques are discussed in this paper and MATLAB simulations presented.
Velocity Field Estimation on Density‐Driven Solute Transport With a Convolutional Neural Network