In the turbulent case, an additional term in the reduced momentum equation will appear. This term corresponds to the projection of the added turbulence modeling term in the momentum equation (in the RANS or the LES formulation at the FOM level) onto the velocity POD modes. The turbulent POD-...
In this work, we propose a new regularization of the 3D Navier–Stokes equations, which we call the 3D velocity–vorticity-Voigt (VVV) model, with a Voigt regularization term added to momentum equation in velocity–vorticity form, but with no regularizing term in the vorticity equation. We ...
In this paper, physics-informed neural network (PINN) based on characteristic-based split (CBS) is proposed, which can be used to solve the time-dependent Navier-Stokes equations (N-S equations). In this method, The output parameters and corresponding losses are separated, so the weights betwe...
The L2(Ω) norm and inner product will be denoted by ‖⋅‖ and (⋅,⋅), respectively, while all other norms will be labeled with subscripts. Denote the natural function spaces for velocity and pressure, respectively, by ≔X≔H01(Ω)d≔Q≔L02(Ω).In X, we have the ...
This section is concerned with an important class of flow problems in which the vorticity is everywhere zero, and for such problems the Navier-Stokes equation may be greatly simplified. For one thing, the viscosity term drops out of it. For another, the nonlinear term, (v· ∇)v, may ...
By minimizing the loss function, this approach allows the output variables to automatically satisfy physical equations without the need for labeled data. The Navier-Stokes equation is one of the most classic governing equations in thermal fluid engineering. This study constructs a PINN to solve the ...
This equation can be treated as the p-adic analog of the Navier–Stokes equation. This is a nonlinear p-adic pseudo-differential equation. The mathematical theory of such equations has not yet been developed (see [11] for one special example). We hope that the presented derivation of ...