From now on, we are mainly interested in the zero mean vector fields, whose relevant Fourier coefficients are labeled by the nonzero wave vectors: throughout the paper we will put (2.1)≔≔D0′≔{v∈D′∣〈v〉=0(i.e., v0=0)};Z0d≔Zd∖{0}. The Sobolev space of zero ...
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-...
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 ...