An artificial viscosity augmented physics-informed neural network for incompressible flow

Physics-informed neural networks(PINNs)are proved methods that are effective in solving some strongly nonlinear partial differential equations(PDEs),e.g.,Navier-Stokes equations,with a small amount of boundary or interior data.However,the feasibility of applying PINNs to the flow at moderate or high Reynolds numbers has rarely been reported.The present paper proposes an artificial viscosity(AV)-based PINN for solving the forward and inverse flow problems.Specifically,the AV used in PINNs is inspired by the entropy viscosity method developed in conventional computational fluid dynamics(CFD)to stabilize the simulation of flow at high Reynolds numbers.The newly developed PINN is used to solve the forward problem of the two-dimensional steady cavity flow at Re=1000 and the inverse problem derived from two-dimensional film boiling.The results show that the AV augmented PINN can solve both problems with good accuracy and substantially reduce the inference errors in the forward problem.

Multiple solutions and hysteresis in the flows driven by surface with antisymmetric velocity profile

Multiple steady solutions and hysteresis phenomenon in the square cavity flows driven by the surface with antisymmetric velocity profile are investigated by numerical simulation and bifurcation analysis.A high order spectral element method with the matrix-free pseudo-arclength technique is used for the steady-state solution and numerical continuation.The complex flow patterns beyond the symmetry-breaking at Re≈320 are presented by a bifurcation diagram for Re<2500.The results of stable symmetric and asymmetric solutions are consistent with those reported in literature,and a new unstable asymmetric branch is obtained besides the stable branches.A novel hysteresis phenomenon is observed in the range of 2208<Re<2262,where two pairs of stable and two pairs of unstable asymmetric steady solutions beyond the stable symmetric state coexist.The vortices near the sidewall appear when the Reynolds number increases,which correspond to the bifurcation of topology structure,but not the bifurcation of Navier-Stokes equations.The hysteresis is proposed to be the result of the combined mechanisms of the competition and coalescence of secondary vortices.

A LATTICE BOLTZMANN SUBGRID MODEL FOR LID-DRIVEN CAVITY FLOW

In recent years, the Lattice Boltzmann Method (LBM) has developed into an alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids. In order to propose LBM for high Reynolds number fluid flow applications, a subgrid turbulence model for LBM was introduced based on standard Smagorinsky subgrid model and Lattice Bhatnagar-Gross-Krook (LBGK) model. The subgrid LBGK model was subsequently used to simulate the two-dimensional driven cavity flow at high Reynolds numbers. The simulation results including distribution of stream lines, dimensionless velocities distribution, values of stream function, as well as location of vertex center, were compared with benchmark solutions, with satisfactory agreements.

Least Square Finite Element Method for Viscous Splitting of Unsteady Incompressible Navier–Stokes Equations

In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.