arXiv subjects

Shravan Veerapaneni

Publications and source records attributed to Shravan Veerapaneni.

51 records · Page 3Linked to original sources

arXiv2020

Optimal slip velocities of micro-swimmers with arbitrary axisymmetric shapes

This article presents a computational approach for determining the optimal slip velocities on any given shape of an axisymmetric micro-swimmer suspended in a viscous fluid. The objective is to minimize the power loss to maintain a target swimming speed, or equivalently to maximize the efficiency of the micro-swimmer. Owing to the linearity of the Stokes equations governing the fluid motion, we show that this PDE-constrained optimization problem reduces to a simpler quadratic optimization problem, whose solution is found using a high-order accurate boundary integral method. We consider various families of shapes parameterized by the reduced volume and compute their swimming efficiency. {Among those, prolate spheroids were found to be the most efficient micro-swimmer shapes for a given reduced volume. We propose a simple shape-based scalar metric that can determine whether the optimal slip on a given shape makes it a pusher, a puller, or a neutral swimmer.}

physics.flu-dyn↗

arXiv2020

A scalable computational platform for particulate Stokes suspensions

We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle collisions. This algorithm extends the well-known complementarity method for non-smooth multi-body dynamics to resolve collisions in dense rigid body suspensions. This approach formulates the collision resolution problem as a linear complementarity problem with geometric `non-overlapping' constraints imposed at each timestep. It is then reformulated as a constrained quadratic programming problem and the Barzilai-Borwein projected gradient descent method is applied for its solution. This framework is designed to be applicable for any convex particle shape, e.g., spheres and spherocylinders, and applicable to any Stokes mobility solver, including the Rotne-Prager-Yamakawa approximation, Stokesian Dynamics, and PDE solvers (e.g., boundary integral and immersed boundary methods). In particular, this method imposes Newton's Third Law and records the entire contact network. Further, we describe a fast, parallel, and spectrally-accurate boundary integral method tailored for spherical particles, capable of resolving lubrication effects. We show weak and strong parallel scalings up to $8\times 10^4$ particles with approximately $4\times 10^7$ degrees of freedom on $1792$ cores. We demonstrate the versatility of this framework with several examples, including sedimentation of particle clusters, and active matter systems composed of ensembles of particles driven to rotate.

cs.CE↗

arXiv2020

Simulating cilia-driven mixing and transport in complex geometries

Cilia and flagella are self-actuated microtubule-based structures that are present on many cell surfaces, ranging from the outer surface of single-cell organisms to the internal epithelial surfaces in larger animals. A fast and robust numerical method that simulates the coupled hydrodynamics of cilia and the constituent particles in the fluid such as rigid particles, drops or cells would be useful to not only understand several disease and developmental pathologies due to ciliary dysfunction but also to design microfluidic chips with ciliated cultures for some targeted functionality---e.g., maximizing fluid transport or particle mixing. In this paper, we develop a hybrid numerical method that employs a boundary integral method for handling the confining geometries and the constituent rigid particles and the method of regularized Stokeslets for handling the cilia. We provide several examples demonstrating the effects of confining geometries on cilia-generated fluid mixing as well as the cilia-particle hydrodynamics.

physics.flu-dyn↗

arXiv2020

An Active Learning Framework for Constructing High-fidelity Mobility Maps

A mobility map, which provides maximum achievable speed on a given terrain, is essential for path planning of autonomous ground vehicles in off-road settings. While physics-based simulations play a central role in creating next-generation, high-fidelity mobility maps, they are cumbersome and expensive. For instance, a typical simulation can take weeks to run on a supercomputer and each map requires thousands of such simulations. Recent work at the U.S. Army CCDC Ground Vehicle Systems Center has shown that trained machine learning classifiers can greatly improve the efficiency of this process. However, deciding which simulations to run in order to train the classifier efficiently is still an open problem. According to PAC learning theory, data that can be separated by a classifier is expected to require $\mathcal{O}(1/ε)$ randomly selected points (simulations) to train the classifier with error less than $ε$. In this paper, building on existing algorithms, we introduce an active learning paradigm that substantially reduces the number of simulations needed to train a machine learning classifier without sacrificing accuracy. Experimental results suggest that our sampling algorithm can train a neural network, with higher accuracy, using less than half the number of simulations when compared to random sampling.

cs.LG↗

arXiv2019

Solution of Stokes flow in complex nonsmooth 2D geometries via a linear-scaling high-order adaptive integral equation scheme

We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of evaluating weakly-singular, nearly-singular and hyper-singular integrals to high accuracy. Near-singular integral evaluation, in particular, is done using an extension of the scheme developed in J.~Helsing and R.~Ojala, {\it J. Comput. Phys.} {\bf 227} (2008) 2899--2921. The boundary of the given geometry is ``panelized'' automatically to achieve user-prescribed precision. We show that this adaptive panel refinement procedure works well in practice even in the case of complex geometries with large number of corners. In one example, for instance, a model 2D vascular network with 378 corners required less than 200K discretization points to obtain a 9-digit solution accuracy.

math.NA↗

arXiv2019

Hydrodynamics and rheology of a vesicle doublet suspension

The dynamics of an adhesive two-dimensional vesicle doublet under various flow conditions is investigated numerically using a high-order, adaptive-in-time boundary integral method. In a quiescent flow, two nearby vesicles move slowly towards each other under the adhesive potential, pushing out fluid between them to form a vesicle doublet at equilibrium. A lubrication analysis on such draining of a thin film gives the dependencies of draining time on adhesion strength and separation distance that are in good agreement with numerical results. In a planar extensional flow we find a stable vesicle doublet forms only when two vesicles collide head-on around the stagnation point. In a microfluid trap where the stagnation of an extensional flow is dynamically placed in the middle of a vesicle doublet through an active control loop, novel dynamics of a vesicle doublet are observed. Numerical simulations show that there exists a critical extensional flow rate above which adhesive interaction is overcome by the diverging stream, thus providing a simple method to measure the adhesion strength between two vesicle membranes. In a planar shear flow, numerical simulations reveal that a vesicle doublet may form provided that the adhesion strength is sufficiently large at a given vesicle reduced area. Once a doublet is formed, its oscillatory dynamics is found to depend on the adhesion strength and their reduced area. Furthermore the effective shear viscosity of a dilute suspension of vesicle doublets is found to be a function of the reduced area. Results from these numerical studies and analysis shed light on the hydrodynamic and rheological consequences of adhesive interactions between vesicles in a viscous fluid.

physics.flu-dyn↗

arXiv2019

Shape optimization of Stokesian peristaltic pumps using boundary integral methods

This article presents a new boundary integral approach for finding optimal shapes of peristaltic pumps that transport a viscous fluid. Formulas for computing the shape derivatives of the standard cost functionals and constraints are derived. They involve evaluating physical variables (traction, pressure, etc.) on the boundary only. By emplyoing these formulas in conjuction with a boundary integral approach for solving forward and adjoint problems, we completely avoid the issue of volume remeshing when updating the pump shape as the optimization proceeds. This leads to significant cost savings and we demonstrate the performance on several numerical examples.

math.OC↗

arXiv2018

Electrohydrodynamics of deflated vesicles: budding, rheology and pairwise interactions

The electrohydrodynamics of vesicle suspensions is characterized by studying their pairwise interactions in applied DC electric fields in two dimensions. In the dilute limit, the rheology of the suspension is shown to vary nonlinearly with the electric conductivity ratio of the interior and exterior fluids. The prolate-oblate-prolate transition and other transitionary dynamics observed in experiments and previously confirmed via numerical simulations is further investigated here for smaller reduced areas. When two vesicles are initially un-aligned with the external electric field, three different responses are observed when the key parameters are varied: (i) chain formation--they self-assemble to form a chain that is aligned along the field direction, (ii) circulatory motion--they rotate about each other, (iii) oscillatory motion--they form a chain but oscillate about each other.

cond-mat.soft↗

arXiv2018

Tensor Train accelerated solvers for nonsmooth rigid body dynamics

In the last two decades, increased need for high-fidelity simulations of the time evolution and propagation of forces in granular media has spurred renewed interest in discrete element method (DEM) modeling of frictional contact. Force penalty methods, while economic and accessible, introduce artificial stiffness, requiring small time steps to retain numerical stability. Optimization-based methods, which enforce contacts geometrically through complementarity constraints, allow the use of larger time steps at the expense of solving a nonlinear complementarity problem (NCP) each time step. We review the latest efforts to produce solvers for this NCP, focusing on its relaxation to a cone complementarity problem (CCP) and solution via an equivalent quadratic optimization problem with conic constraints. We distinguish between linearly convergent first order methods and second order methods, which gain quadratic convergence and more robust performance at the expense of the solution of large sparse linear systems. We propose a novel acceleration for the solution of Newton step linear systems in second order methods using low-rank compression based fast direct solvers. We use the Quantized Tensor Train (QTT) decomposition to produce efficient approximate representations of the system matrix and its inverse. This provides a robust framework to accelerate its solution in a direct or a preconditioned iterative method. In a number of numerical tests, we demonstrate that this approach displays sublinear scaling of precomputation costs, may be efficiently updated across Newton iterations as well as across time steps, and leads to a fast, optimal complexity solution of the Newton step. This allows our method to gain an order of magnitude speedups over state-of-the-art preconditioning techniques for moderate to large-scale systems, mitigating the computational bottleneck of second order methods.

math.NA↗

arXiv2018

Boundary integral equation analysis for suspension of spheres in Stokes flow

We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical expressions for evaluating the operators away from the boundary. When two particle are located close to each other, we use a truncated series expansion to compute the hydrodynamic interaction. On the other hand, we use the standard spectrally accurate quadrature scheme to evaluate smooth integrals on the far-field, and accelerate the resulting discrete sums using the fast multipole method (FMM). We employ this discretization scheme to analyze several boundary integral formulations of interest including those arising in porous media flow, active matter and magneto-hydrodynamics of rigid particles. We provide numerical results verifying the accuracy and scaling of their evaluation.

math.NA↗

arXiv2016

A unified integral equation scheme for doubly-periodic Laplace and Stokes boundary value problems in two dimensions

We present a spectrally-accurate scheme to turn a boundary integral formulation for an elliptic PDE on a single unit cell geometry into one for the fully periodic problem. Applications include computing the effective permeability of composite media (homogenization), and microfluidic chip design. Our basic idea is to exploit a small least squares solve to apply periodicity without ever handling periodic Green's functions. We exhibit fast solvers for the two-dimensional (2D) doubly-periodic Neumann Laplace problem (flow around insulators), and Stokes non-slip fluid flow problem, that for inclusions with smooth boundaries achieve 12-digit accuracy, and can handle thousands of inclusions per unit cell. We split the infinite sum over the lattice of images into a directly-summed "near" part plus a small number of auxiliary sources which represent the (smooth) remaining "far" contribution. Applying physical boundary conditions on the unit cell walls gives an expanded linear system, which, after a rank-1 or rank-3 correction and a Schur complement, leaves a well-conditioned square system which can be solved iteratively using fast multipole acceleration plus a low-rank term. We are rather explicit about the consistency and nullspaces of both the continuous and discretized problems. The scheme is simple (no lattice sums, Ewald methods, nor particle meshes are required), allows adaptivity, and is essentially dimension- and PDE-independent, so would generalize without fuss to 3D and to other non-oscillatory elliptic problems such as elastostatics. We incorporate recently developed spectral quadratures that accurately handle close-to-touching geometries. We include many numerical examples, and provide a software implementation.

math.NA↗

arXiv2016

Dynamics of a multicomponent vesicle in shear flow

We study the fully nonlinear, nonlocal dynamics of two-dimensional multicomponent vesicles in a shear flow with matched viscosity of the inner and outer fluids. Using a nonstiff, pseudo-spectral boundary integral method, we investigate dynamical patterns induced by inhomogeneous bending for a two phase system. Numerical results reveal that there exist novel phase-treading and tumbling mechanisms that cannot be observed for a homogeneous vesicle. In particular, unlike the well-known steady tank-treading dynamics characterized by a fixed inclination angle, here the phase-treading mechanism leads to unsteady periodic dynamics with an oscillatory inclination angle. When the average phase concentration is around 1/2, we observe tumbling dynamics even for very low shear rate, and the excess length required for tumbling is significantly smaller than the value for the single phase case. We summarize our results in phase diagrams in terms of the excess length, shear rate, and concentration of the soft phase. These findings go beyond the well known dynamical regimes of a homogeneous vesicle and highlight the level of complexity of vesicle dynamics in a fluid due to heterogeneous material properties.

cond-mat.soft↗

arXiv2016

An integral equation formulation for rigid bodies in Stokes flow in three dimensions

We present a new derivation of a boundary integral equation (BIE) for simulating the three-dimensional dynamics of arbitrarily-shaped rigid particles of genus zero immersed in a Stokes fluid, on which are prescribed forces and torques. Our method is based on a single-layer representation and leads to a simple second-kind integral equation. It avoids the use of auxiliary sources within each particle that play a role in some classical formulations. We use a spectrally accurate quadrature scheme to evaluate the corresponding layer potentials, so that only a small number of spatial discretization points per particle are required. The resulting discrete sums are computed in $\mathcal{O}(n)$ time, where $n$ denotes the number of particles, using the fast multipole method (FMM). The particle positions and orientations are updated by a high-order time-stepping scheme. We illustrate the accuracy, conditioning and scaling of our solvers with several numerical examples.

math.NA↗

arXiv2015

A fast algorithm for simulating multiphase flows through periodic geometries of arbitrary shape

This paper presents a new boundary integral equation (BIE) method for simulating particulate and multiphase flows through periodic channels of arbitrary smooth shape in two dimensions. The authors consider a particular system---multiple vesicles suspended in a periodic channel of arbitrary shape---to describe the numerical method and test its performance. Rather than relying on the periodic Green's function as classical BIE methods do, the method combines the free-space Green's function with a small auxiliary basis, and imposes periodicity as an extra linear condition. As a result, we can exploit existing free-space solver libraries, quadratures, and fast algorithms, and handle a large number of vesicles in a geometrically complex channel. Spectral accuracy in space is achieved using the periodic trapezoid rule and product quadratures, while a first-order semi-implicit scheme evolves particles by treating the vesicle-channel interactions explicitly. New constraint-correction formulas are introduced that preserve reduced areas of vesicles, independent of the number of time steps taken. By using two types of fast algorithms, (i) the fast multipole method (FMM) for the computation of the vesicle-vesicle and the vesicle-channel hydrodynamic interaction, and (ii) a fast direct solver for the BIE on the fixed channel geometry, the computational cost is reduced to $O(N)$ per time step where $N$ is the spatial discretization size. Moreover, the direct solver inverts the wall BIE operator at $t = 0$, stores its compressed representation and applies it at every time step to evolve the vesicle positions, leading to dramatic cost savings compared to classical approaches. Numerical experiments illustrate that a simulation with $N=128, 000$ can be evolved in less than a minute per time step on a laptop.

math.NA↗

arXiv2015

Simple and efficient representations for the fundamental solutions of Stokes flow in a half-space

We derive new formulas for the fundamental solutions of slow, viscous flow, governed by the Stokes equations, in a half-space. They are simpler than the classical representations obtained by Blake and collaborators, and can be efficiently implemented using existing fast solvers libraries. We show, for example, that the velocity field induced by a Stokeslet can be annihilated on the boundary (to establish a zero slip condition) using a single reflected Stokeslet combined with a single Papkovich-Neuber potential that involves only a scalar harmonic function. The new representation has a physically intuitive interpretation.

physics.flu-dyn↗