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The algorithm based on integration over Lefschetz thimbles is a promising method to resolve the sign problem for complex actions. However, this algorithm often meets a difficulty in actual Monte Carlo calculations because the configuration…
The gradient flow is a valuable tool for the lattice community, with applications from scale-setting to implementing chiral fermions. Here I focus on the gradient flow as a means to suppress power-divergent mixing. Power-divergent mixing…
We develop a reduced-order framework for optimizing mixing in two-dimensional incompressible flows. Instead of optimizing the full transport PDE, the method maximizes the length of advected material interfaces, leading to a…
Mixing by incompressible flows is a ubiquitous yet incompletely understood phenomenon in fluid dynamics. While previous studies have focused on optimal mixing rates, the question of its genericity, i.e., whether mixing occurs for typical…
In this paper, we consider the passive scalar solutions in shear flows with critical points. With a detailed hypocoercivity functional, we develop streamline-wise enhanced dissipation estimates.
Consistent splitting schemes are among the most accurate pressure segregation methods, incurring no splitting errors or spurious boundary conditions. Nevertheless, their theoretical properties are not yet fully understood, especially when…
Three-dimensional laminar flow structures with mixing, chemical reaction, normal strain, and shear strain qualitatively representative of turbulent combustion at the small scales are analyzed. A mixing layer is subjected to counterflow in…
For time-dependent problems with high-contrast multiscale coefficients, the time step size for explicit methods is affected by the magnitude of the coefficient parameter. With a suitable construction of multiscale space, one can achieve a…
We study diffusion and mixing in different linear fluid dynamics models, mainly related to incompressible flows. In this setting, mixing is a purely advective effect which causes a transfer of energy to high frequencies. When diffusion is…
Convergence failure and slow convergence rates are among the biggest challenges with solving the system of non-linear equations numerically. Although mitigated, such issues still linger when using strictly small time steps and…
We investigate statistical properties of the passive scalar near boundaries (walls) in random (turbulent) flows assuming weakness of its diffusion. Then at advanced stages of the passive scalar mixing its unmixed residue is concentrated in…
A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix or stir ideal fluid, and can give rise to interesting flow patterns. Assuming these systems of fluid stirrers are two-dimensional, the…
Mixing by cutting-and-shuffling can be understood and predicted using dynamical systems based tools and techniques. In existing studies, mixing is generated by maps that repeat the same cut-and-shuffle process at every iteration, in a…
Consider a passive scalar which is advected by an incompressible flow $u$ and has small molecular diffusivity $\kappa$. Previous results show that if $u$ is exponentially mixing and $C^1$, then the dissipation time is $O(|\log \kappa|^2)$.…
Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…
We apply lattice Boltzmann method to study the phase separation of a two-dimensional binary fluid mixture in shear flow. The algorithm can simulate systems described by the Navier-Stokes and convection-diffusion equations. We propose a new…
This paper considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The invariance of the feasible…
We analyze the dynamics of solute mixing in a vortex flow. The transport of a passive tracer is considered in a Rankine vortex. The action of a shear flow, in general, is to achieve stretching of fluid elements. A vortex flow exhibits…
A Lagrangian method for the numerical simulation of the Kraichnan passive scalar model is introduced. The method is based on Monte--Carlo simulations of tracer trajectories, supplemented by a point-splitting procedure for coinciding points.…
A sensitive porosity adjoint method (SPAM) for optimizing the topology of fluid machines has been proposed. A sensitivity function with respect to the porosity has been developed. In the first step of the optimization process, porous media…