03/30/2022
By Sokny Long

The Francis College of Engineering, Department of Mechanical Engineering, invites you to attend a Master’s thesis defense by Jairo Vanegas on “Understanding Lagrangian-to-Eulerian Coupling Errors Using Kernel Density Estimation.”

MSE Candidate: Jairo Vanegas
Defense Date: Tuesday, April 12, 2022
Time: Noon to 1:50 p.m. EST
Location: Shah Hall 306. This will be a hybrid defense with the option to attend via Zoom. Those interested in attending should contact jairo_vanegas@student.uml.edu and committee advisor, noah_vandam@uml.edu, at least 24 hours prior to the defense to request access to the virtual meeting.

Committee Chair (Advisor): Noah Van Dam, Assistant Professor, Department of Mechanical Engineering, University of Massachusetts Lowell

Committee Members:

  • David Willis, Associate Professor, Department of Mechanical Engineering, University of Massachusetts Lowell
  • Juan Trelles, Associate Professor, Department of Mechanical Engineering, University of Massachusetts Lowell

Brief Abstract:
Stochastic Lagrangian-Eulerian (LE) methods are one of the most common used to simulate fuel sprays due to their computational efficiency in modeling dilute, dispersed multiphase flows. However, theoretical analyses of these methods' consistency and convergence have been limited. This work presents a generalized expression for the Lagrangian-to-Eulerian coupling error with second-order coupling kernels, which includes all strictly-positive kernels. The derived expressions shows that convergence behavior is independent of the specific kernel used, but different kernels may have different absolute error magnitudes due to different kernel properties. The derived error expression contains two terms, a statistical error term proportional to kernel roughness, and a spatial error term proportional to the kernel variance. Smoother kernels such as the Gaussian kernel are shown to have lower statistical errors, but larger spatial errors for a constant smoothing parameter width/cell size.

Additional empirical tests were run using a 2D static test case to validate the analytical developments. The empirical test results support the analytical developments, including the trade-off between statistical and spatial errors between different coupling kernels. The empirical tests also revealed boundary errors where the Gaussian kernel extended beyond the edge of the domain. Boundary correction methods are investigated to analyze and reduce the boundary error, showing good performance for a slight increase in computational costs.

The error expressions discussed in this thesis may be used to provide analytical error estimates to future LE simulations which may be used as part of error-control strategies do dynamically adjust local Eulerian cell size, Lagrangian parcel count, and/or coupling kernel properties to minimize computational cost while meeting specified error bounds.

All interested students and faculty members are invited to attend the online defense via remote access.