Solving the Poisson equation for pressure has been known to be the bottleneck in pressure-correction algorithms, taking up to 50% of the total computation time.

In this work, we examine the driving factors that contribute to the reduction in traditional multigrid performance, where we find the persistence of highly oscillatory modes in the error near the interface inhibits convergence. 

Therefore, we develop a Local Poisson Preconditioner that locally employs over-relaxation on the system, quickly providing a highly accurate preconditioned solution for the Pressure Poisson equation. Our method is benchmarked on a variety of canonical multiphase flow problems of various density ratios, on various mesh types, showing the robustness of our Local Poisson Preconditioner.

We examine the dynamics and interactions of bubble ensemble pairs and triplets as they rise under a variety of conditions. We focus on the role of the initial lateral and vertical displacements, Bond number (Bo), and number of bubbles (two or three). Our results show that for the rise of a lateral pair of bubbles, enhanced horizontal oscillations in the rise are exhibited at Bo heightened Bo. Bubbles initially positioned close to each other exhibit a strong repulsive force, increasing the separation distance between the two early on in their rise. At constant Bo and for a long enough rise time, each bubble pair reaches an equilibrium lateral separation distance. Finally, we note the presence of a vertical bubble positioned above the two laterally displaced bubbles inhibits the lateral separation of the two trailing bubbles and in instances of small initial vertical separation, the bubble triplet will coalesce during its rise.

Buoyancy-driven convection, also known as natural convection or free convection, is a mode of heat transfer and fluid motion that is driven by variations in density within the fluid. This process occurs in various environments (Ocean circulation, Weather Systems, Planetary convection), and industrial processes (heat exchangers, power systems, electronics cooling, building ventilation). In these works, we explore the role of the Prandtl number on the formation of vortices, convective mode generation, and instability in the Differentially Heated Cavity configuration. Our results point to an enhanced number of vortices and strengthening roles of vorticity and convection in the limit of low Pr.

We expand our investigations to explore the role of narrow-slot configuration on thermal performance, flow field, and heat transfer performance in the DHC cell of the vertical aspect ratio of 1/4. Our results point to an elevated influence in the narrow walls in the limit of low Pr, especially on the velocity field and magnitudes, thermal field, and heat transfer performance 

In channel flow, unsteadiness and turbulence often arise when the flow velocity exceeds a certain critical value, known as the critical Reynolds number. Beyond this threshold, small disturbances in the fluid can grow and amplify, leading to the formation of vortices, swirls, eddies, and other complex flow structures.

In this investigation, we employ a pseudo-spectral method to examine the onset of unsteadiness and turbulence in channel flow, mainly focusing on the Q-criterion (a). Q-criterion is commonly used to identify and visualize complex flow structures and is defined as the summation of the antisymmetric and symmetric components of the velocity gradient tensor. Q is the balance between the rotation and the strain rates of the flow, where rotational motion dominates for isosurfaces where Q > 0, while the deformation motion dominates for isosurfaces where Q < 0.

Illustrated to the left are a series of isosurfaces of Q colored by the horizontal velocity magnitude at Re = 3000. (b) Q = -1/2 (c) Q = 1/2