We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even when strong vortices or backflows occur at the outflow boundary. Under certain situations it can be reduced to a form that can be analogized to the usual convective boundary condition. One prominent feature of this boundary condition is that it provides a control over the velocity on the outflow/open boundary. This is not available with the other energy-stable open boundary conditions from previous works. Our numerical algorithm treats the proposed open boundary condition based on a rotational velocity-correction type strategy. It gives rise to a Robin-type condition for the discrete pressure and a Robin-type condition for the discrete velocity on the outflow/open boundary, respectively at the pressure and the velocity sub-steps. We present extensive numerical experiments on a canonical wake flow and a jet flow in open domain to test the effectiveness and performance of the method developed herein. Simulation results are compared with the experimental data as well as with other previous simulations to demonstrate the accuracy of the current method. Long-time simulations are performed for a range of Reynolds numbers, at which strong vortices and backflows occur at the outflow/open boundaries. The results show that our method is effective in overcoming the backflow instability, and that it allows for the vortices to discharge from the domain in a fairly natural fashion even at high Reynolds numbers.
We present a numerical method for the solution of interfacial growth governed by the Stefan model coupled with incompressible fluid flow. An algorithm is presented which takes special care to enforce sharp interfacial conditions on the temperature, the flow velocity and pressure, and the interfacial velocity. The approach utilizes level-set methods for sharp and implicit interface tracking, hybrid finite-difference/finite-volume discretizations on adaptive quadtree grids, and a pressure-free projection method for the solution of the incompressible Navier-Stokes equations. The method is first v…
We propose two Hybrid High-Order (HHO) methods for the incompressible Navier-Stokes equations and investigate their robustness with respect to the Reynolds number. While both methods rely on a HHO formulation of the viscous term, the pressure-velocity coupling is fundamentally different, up to the point that the two approaches can be considered antithetical. The first method is kinetic energy preserving, meaning that the skew-symmetric discretization of the convective term is guaranteed not to alter the kinetic energy balance. The approximated velocity fields exactly satisfy the divergence fre…
We present an energy-stable scheme for simulating the incompressible Navier-Stokes equations based on the generalized Positive Auxiliary Variable (gPAV) framework. In the gPAV-reformulated system the original nonlinear term is replaced by a linear term plus a correction term, where the correction term is put under control by an auxiliary variable. The proposed scheme incorporates a pressure-correction type strategy into the gPAV procedure, and it satisfies a discrete energy stability property. The scheme entails the computation of two copies of the velocity and pressure within a time step, by …
Wind tunnel experiments were conducted to study the impact of atmospheric stratification on flow and dispersion within and over a regular array of rectangular buildings. Three stable and two convective incoming boundary layers were tested with a Richardson number ranging from $-$1.5 to 0.29. Dispersion measurements were carried using a fast response flame ionisation detector. The results show that the stratification effect on the plume width is significantly lower than the effect on the vertical profiles. Stable stratification did not affect the plume central axis inside the canopy, but in the…
Varieties of energy-stable numerical methods have been developed for incompressible two-phase flows based on the Navier-Stokes-Cahn-Hilliard (NSCH) model in the Eulerian framework, while few investigations have been made in the Lagrangian framework. Smoothed particle hydrodynamics (SPH) is a popular mesh-free Lagrangian method for solving complex fluid flows. In this paper, we present a pioneering study on the energy-stable SPH discretization of the NSCH model for incompressible two-phase flows. We prove that this SPH method inherits mass and momentum conservation and energy dissipation proper…
A novel reduced-order model (ROM) formulation for incompressible flows is presented with the key property that it exhibits non-linearly stability, independent of the mesh (of the full order model), the time step, the viscosity, and the number of modes. The two essential elements to non-linear stability are: (1) first discretise the full order model, and then project the discretised equations, and (2) use spatial and temporal discretisation schemes for the full order model that are globally energy-conserving (in the limit of vanishing viscosity). For this purpose, as full order model a staggere…
An Unconditionally Energy-Stable Scheme Based on an Implicit Auxiliary Energy Variable for Incompressible Two-Phase Flows with Different Densities Involving Only Precomputable Coefficient Matrices
Non-isothermal particles suspended in a fluid lead to complex interactions -- the particles respond to changes in the fluid flow, which in turn is modified by their temperature anomaly. Here, we perform a novel proof-of-concept numerical study based on tracer particles that are thermally coupled to the fluid. We imagine that particles can adjust their internal temperature reacting to some local fluid properties and follow simple, hard-wired active control protocols. We study the case where instabilities are induced by switching the particle temperature from hot to cold depending on whether it …
We present an unconditionally energy-stable scheme for approximating the incompressible Navier-Stokes equations on domains with outflow/open boundaries. The scheme combines the generalized Positive Auxiliary Variable (gPAV) approach and a rotational velocity-correction type strategy, and the adoption of the auxiliary variable simplifies the numerical treatment for the open boundary conditions. The discrete energy stability of the proposed scheme has been proven, irrespective of the time step sizes. Within each time step the scheme entails the computation of two velocity fields and two pressure…
In this paper non-neutral approaching flows were employed in a meteorological wind tunnel on a regular urban-like array of rectangular buildings. As far as stable stratification is concerned, results on the flow above and inside the canopy show a clear reduction of the Reynolds stresses and an increment of the Monin-Obukhov length up to 80%. The roughness length and displacement height were also affected, with a reduction up to 35% for the former and an increment up to 12% for the latter. A clear reduction of the turbulence within the canopy was observed. In the convective stratification cases…
In close two-body astrophysical systems, such as binary stars or Hot Jupiter systems, tidal interactions often drive dynamical evolution on secular timescales. Many host stars and presumably giant gaseous planets feature a convective envelope. Tidal flows generated therein by the tidal potential of the companion can be dissipated through viscous friction, leading to the redistribution and exchange of angular momentum within the convective shell and with the companion, respectively. In the tightest systems, nonlinear effects are likely to have a significant impact on the tidal dissipation and t…
In the context of flow visualization a triple decomposition of the velocity gradient into irrotational straining flow, shear flow and rigid body rotational flow was proposed by Kolar in 2007 [V. Kolar, International journal of heat and fluid flow, 28, 638, (2007)], which has recently received renewed interest. The triple decomposition opens for a refined energy stability analysis of the Navier-Stokes equations, with implications for the mathematical analysis of the structure, computability and regularity of turbulent flow. We here perform an energy stability analysis of turbulent incompressibl…
Magnetic fields vary in complexity for different stars. The stability of dipolar magnetic fields is known to depend on different quantities, e.g., the stellar rotation, the stratification, and the intensity of convective motions. Here, we study the dipolar stability in a system with an inner stable zone. We present preliminary results of dynamo simulations using the Rayleigh number as a control parameter. The stiffness of the stable zone is accordingly varied to keep a constant ratio of the Brunt-Vaisala frequency to the angular velocity. Similarly to the completely convective spherical shell,…
The treatment of complex geometries in Computational Fluid Dynamics applications is a challenging endeavor, which immersed boundary and cut-cell techniques can significantly simplify by alleviating the meshing process required by body-fitted meshes. These methods however introduce new challenges, as the formulation of accurate and well-posed discrete operators becomes nontrivial. Here, a conservative cartesian cut cell method is proposed for the solution of the incompressible Navier--Stokes equation on staggered Cartesian grids. Emphasis is set on the structure of the discrete operators, desig…
The diffusion of a solute from a concentrated source into a horizontal, stationary, fluid-saturated porous medium can lead to a convective motion when a gravitationally unstable density stratification evolves. In an inclined porous medium, the convective flow becomes intricate as it originates from a combination of diffusion and lateral flow, which is dominant near the source of the solute. Here, we investigate the role of inclination on the onset of convective instability by linear stability analyses of Darcy's law and mass conservation for the flow and the concentration field. We find that t…
The prohibitive cost and low fidelity of experimental data in industry scale thermofluid systems limit the usefulness of pure data-driven machine learning methods. Physics-informed neural networks (PINN) strive to overcome this by embedding the physics equations in the construction of the neural network loss function. In the present paper, the mixed-variable PINN methodology is applied to develop steady-state and transient surrogate models of incompressible laminar flow with heat transfer through a 2D internal domain with obstructions. Automatic spatial and temporal differentiation is applied …
We present a strong form, meshless point collocation explicit solver for the numerical solution of the transient, incompressible, viscous Navier-Stokes (N-S) equations in two dimensions. We numerically solve the governing flow equations in their stream function-vorticity formulation. We use a uniform Cartesian embedded grid to represent the flow domain. We compute the spatial derivatives using the Meshless Point Collocation (MPC) method. We verify the accuracy of the numerical scheme for commonly-used benchmark problems including lid-driven cavity flow, flow over a backward-facing step and vor…
Here we report some interesting new features of the spatio-temporal instability of the incompressible plane Couette-Poiseuille flow (CPF). First of all, this flow represents the first instance of a "non-inflectional" absolute instability, within constant-viscosity formulation, which is triggered when one of the plates moves opposite to the bulk motion. More strikingly, with further increase in the negative plate motion, the absolute instability ($\textrm{AI}$) transitions to an "upstream" convective instability ($\textrm{CI}^-$), wherein an unstable wave packet moves opposite to the direction …
In close exoplanetary systems, tidal interactions drive orbital and spin evolution of planets and stars over long timescales. Tidally-forced inertial waves (restored by the Coriolis acceleration) in the convective envelopes of low-mass stars and giant gaseous planets contribute greatly to the tidal dissipation when they are excited and subsequently damped (e.g. through viscous friction), especially early in the life of a system. These waves are known to be subject to nonlinear effects, including triggering differential rotation in the form of zonal flows. In this study, we use a realistic tida…
The existence of a stably stratified layer underneath the core-mantle boundary (CMB) has been recently revived by corroborating evidences coming from seismic studies, mineral physics and thermal evolution models. Such a layer could find its physical origination either in compositional stratification due to the accumulation of light elements at the top or the core or in thermal stratification due to the heat flux becoming locally sub-adiabatic. The exact properties of this stably-stratified layer, namely its size $\mathcal{H}_S$ and the degree of its stratification characterised by the Brunt-Vä…
