integrated with sparsity-promoting techniques (such as SINDy15and proposed symmetric invariant SINDy) to identify dimensionally homogeneous differential equations and dimensionless numbers from data. The analyse
The dimensionless governing equations for a particle-laden incompressible turbulent flow are the Navier–Stokes equations: • mass conservation, (3.14)∂uj∂xj=0, • momentum conservation, (3.15)∂uj∂t+∂(ujuk)∂xk=−∂p∂xj+ν∂2uj∂xk∂xk+fj, where j=1,2,3 ind...
These challenges influence the development of forward numerical models of turbidity currents and their resulting submarine fans. Some of these models carry large computational costs to solve Navier-Stokes equations for complex and fully turbulent turbidity currents. On the other side of the spectrum are...
2.3.3 The Navier-Stokes equation So far, we have discussed fluid viscosity and some of the dimensionless numbers that are important for understanding fluid flow in microfluidic channels. We also established that laminar flow dominates in microfluidic systems. At the microscale, the properties of lami...
problem involving Marangoni convection. The governing equations are Navier-Stokes and The energy Eqn. I am trying to benchmark against data in the literature but my data points are all out by a constant factor, so I am assuming I have made some error in the non-dimensionalisation of the ...
The governing equations are Navier-Stokes and The energy Eqn. I am trying to benchmark against data in the literature but my data points are all out by a constant factor, so I am assuming I have made some error in the non-dimensionalisation of the problem. The original eqns were non-...
The dynamics of magnetic fields (see for an introduction Moffatt [1978], Parker [1979], Soward [1983]) has many similarities with Navier-Stokes turbulence: recall the Batchelor analogy between vorticity and induction, both undergoing stretching through velocity gradients. Hence, one expects growth of...
Compatibility and mutual interaction among the dimensionless groups present in the navier-stokes and energy differential equationsMolecular modellingNucleotidesPurinergic receptorsP2X receptor agonistsP2X receptor antagonistsP2X receptorsA method is proposed for obtaining a compatibility relationship among the ...
For accurate prediction of the swirling flow in a cyclone, the Large Eddy Simulation (LES) technique was applied. Since even large-scale cyclones operate at low Mach numbers, the gas flow in a cyclone was modelled as an isothermal incompressible flow and the following filtered Navier-Stokes equ...
The Knudsen number, Kn, is a number useful in defining the lower limit in length scale where the Navier–Stokes equations are relevant and the transitions to other forms of transport in micron- to nanometre- scale flow channels. Kn is defined as the ratio of the mean-free-path, π, of ...