David Kamensky

Overview

My research is interdisciplinary, with the unifying theme of exploring the use of flexible, automation-friendly representations of geometry in physics-based computer simulations. This work aims to address the current bottleneck in computational mechanics, namely that analysts spend a substantial amount of their time on geometry manipulation, which drives up the cost of applying computer simulation to design, optimize, or predict behavior of physical systems. Eliminating the need for manual intervention by analysts will ultimately enable artificial intelligent agents to set up, execute, and learn from physics-based simulations, contributing to automation of broader tasks, such as engineering design, scientific inquiry, and technically-informed decision-making. I have worked on a number of different numerical methods and applications, as discussed below.

If you think you might be interested in participating in this research, check for openings under "Team and openings", and/or contact me directly via email.

Numerical methods

Many phenomena in fluid and solid mechanics are modeled by partial differential equation (PDE) systems that would be intractable to solve by hand. Thus, approximate PDE solutions are sought by numerical methods, which is the technical basis for computer simulation of mechanics. Some classes of numerical methods that I am actively researching are:

Isogeometric analysis (IGA): Generalizing finite element analysis to allow seamless integration with computer-aided design (CAD).
Immersogeometric analysis (IMGA): Extending IGA to handle complex geometries formed by intersections of curves, surfaces, and volumes, as found in most industrial CAD models.
Meshfree methods: Using point cloud representations of geometry in computer simulations.

Software

For numerical methods to have an impact on science and engineering, they must be implemented as computer programs. Publicly-available components of my research software are available on GitHub. In particular, I am actively developing tIGAr, which is a library for using the finite element automation software FEniCS to perform IGA. Other projects involve more specialized research codes, some of which may eventually be developed into open-source projects.

Figure: Applications of tIGAr include shell structure analysis of heart valves and turbulent flow. It can be used in large-scale isogeometric computations, on high-performance parallel supercomputers.

Related publications:

Explaining the technical principles behind tIGAr: https://doi.org/10.1016/j.cma.2018.10.002
An extension of tIGAr for immersogeometric analysis of fluid–thin structure interaction: https://doi.org/10.1016/j.camwa.2020.01.023

Applications

Much of my work relates specifically to computational fluid–structure interaction (FSI), and/or issues specific to the fluid and structure subproblems. Several applications are highlighted below.

Multidisciplinary design, analysis, and optimization of electric air taxis

There is a current surge of interest in electric vertical takeoff and landing (eVTOL) aircraft, for use in urban air mobility. However, the design space of such aircraft is not thoroughly explored. Potential viable designs may have radically-different layouts and involve coupling between structural mechanics, aerodynamics, acoustics, electromagnetic fields in motors, battery chemistry, heat diffusion, and other physical phenomena. As such, optimization within this space will require novel analysis tools that are highly flexible with respect to both geometry and physical modeling. Under a recent multi-PI NASA project, my group will combine i(mmer)sogeometric analysis and automated code generation to produce tools for multiphysics analysis of eVTOL aircraft, contributing to a broader framework for multidisciplinary design, analysis, and optimization (MDAO), using the OpenMDAO library to coordinate between disciplines.

Figure: eVTOL geometry in NASA's Open Vehicle Sketch Pad (OpenVSP) and IGA of a wing, with coupling at arbitrary surface intersections.

Related publications:

MDAO of thermomechanics in eVTOL batteries: https://doi.org/10.2514/6.2021-3068
IGA of shell structures with non-matching parts: https://doi.org/10.1016/j.camwa.2022.02.007
Code generation for multidisciplinary topology optimization: https://doi.org/10.1007/s00158-022-03168-2

Collaborating PIs: J. T. Hwang (UCSD), H. A. Kim (UCSD), Y. S. Meng (UCSD), J. T. Chambers (Aurora), C. Mi (SDSU), A. Ning (BYU), T. Winter (M4), S. K. Lee (UC Davis)

Computational biomechanics

Bioprosthetic heart valves (BHVs) are artificial replacements for diseased heart valves. Durability of these devices is currently limited; extending it will require insight into the FSI dynamics of the valves, which are passive structures driven by forces from the surrounding hemodynamics. My work on this introduced the concept of immersogeometric analysis (IMGA), and I developed a new immersed-boundary type numerical method based on the novel dynamic augmented Lagrangian (DAL) algorithm, to perform IMGA of BHV FSI. The application of IMGA to this problem has allowed for direct use of CAD models of BHVs in FSI simulations, greatly simplifying the process of setting up and running calculations.

Figure: Comparison of artificial valve simulations with results from an in vitro experiment. See this paper for details.

Related publications:

Introducing the the term IMGA and (what we now call) the DAL numerical approach: https://doi.org/10.1016/j.cma.2014.10.040
Studying the effect of arterial elasticity on valve dynamics: https://doi.org/10.1007/s00466-014-1059-4
Stabilizing the DAL method: https://doi.org/10.4208/cicp.150115.170415s
Integrating DAL-based IMGA with CAD: https://doi.org/10.1007/s00466-015-1166-x
Applying isogeometric discrete differential forms to improve mass conservation in IMGA: https://doi.org/10.1016/j.cma.2016.07.028
Enhancing the conservation properties of DAL: https://doi.org/10.1016/j.camwa.2017.07.006
A nonlocal contact formulation applied to atrioventricular valve simulation (see below): https://doi.org/10.1016/j.cma.2017.11.007
Applying DAL-based IMGA to patient-specific valve design: https://doi.org/10.1002/cnm.2938
Constitutive modeling of BHV leaflets: https://doi.org/10.1016/j.jbiomech.2018.04.012
Convergence analysis of the DAL numerical approach: https://doi.org/10.1142/S0218202518500537

Collaborating PIs: M.-C. Hsu (Iowa State), Y. Yu (Lehigh), J. A. Evans (CU Boulder), Y. Bazilevs (Brown), M. S. Sacks (UT Austin), T. J. R. Hughes (UT Austin)

Extreme event simulation

In collaboration with the UCSD Center for Extreme Events (CEER), I have worked on combining IGA and meshfree methods to simulate highly-dynamic loading of fluid–solid continua, e.g., to predict effects of blast loads on structures. This effort combines IGA of high-mach-number compressible flows with meshfree analysis of inelastic solids, including fragmentation. As part of this work, I developed a new phase-field model for fracture mechanics that yields a hyperbolic system of partial differential equations. Efficient and flexible simulation of extreme events is more challenging from the perspective of computer science; ongoing work uses parallel graph data structures to simultaneously parallelize the meshfree structure and isogeometric fluid discretizations.

Figure: Isogeometric–meshfree analysis of a structure fragmenting due to blast loading. The stabilized fluid formulation captures sharp shocks in the air flow. Use of a phase-field fracture model allows cracks to nucleate and branch without a priori knowledge of their paths. See this paper for details.

Related publications:

Introducing the isogeometric–meshfree blast FSI framework: https://doi.org/10.1007/s00466-017-1395-2
Developing a phase-field fracture formulation suitable for explicit hydrocodes: https://doi.org/10.1016/j.jmps.2018.07.010
Extending the isogeometric–meshfree framework to include phase-field fracture: https://doi.org/10.1016/j.jmps.2018.07.008
Adapting the idea of residual-based shock capturing viscosity to solid mechanics: https://doi.org/10.1016/j.cma.2019.112638

Collaborating PIs: G. Moutsanidis (Stony Brook), J. S. Chen (UCSD), Y. Bazilevs (Brown)

Nonlocal modeling of contact mechanics

I have recently worked on developing geometrically-flexible methods for analyzing situations with structural (self-)contact. The contact forces derive from a nonlocal model similar to peridynamics. This contact model is then discretized in a meshfree way, which dramatically simplifies collision detection, but remains compatible with mesh-based or isogeometric discretizations of the structure's elastodynamics. A simplified implementation is available as a demo in tIGAr.

Figure: Nonlocal contact modeling applied to benchmark problems and simulation of an atrioventricular heart valve.

Related publications:

Introducing the nonlocal contact model and applying it to atrioventricular valve simulation: https://doi.org/10.1016/j.cma.2017.11.007
Relating the model to peridynamics and generalizing it to include friction: https://doi.org/10.1007/s42102-019-00012-y
A review of nonlocal methods for contact mechanics: https://doi.org/10.1007/978-3-030-87312-7_23

Collaborating PIs: M.-C. Hsu (Iowa State), C.-H. Lee (Oklahoma State), J. Yan (Urbana–Champaign), Y. Bazilevs (Brown)

Turbulent industrial flows

I have worked on applying computational fluid dynamics (CFD) to analysis and optimization of various industrial systems involving turbulent flows. Turbulence is modeled through variational multiscale (VMS) formulations of the incompressible and compressible Navier–Stokes equations. Some of these CFD problems benefited from using the finite cell method (FCM) to manage geometric complexity.

Related publications:

Optimizing a hydraulic arresting gear with DAL-based IMGA: https://doi.org/10.1016/j.compfluid.2015.12.004
Studying flow around an agricultural tractor using FCM-based IMGA: https://doi.org/10.1016/j.compfluid.2015.08.027
Stabilized finite element analysis of compressible flow on moving domains, including a gas turbine: https://doi.org/10.1016/j.compfluid.2017.02.006

Collaborating PIs: M.-C. Hsu (Iowa State), Dominik Schillinger (Hannover), Y. Bazilevs (Brown)

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