Recent Submissions

(Computer Methods in Applied Mechanics and Engineering, 2019-04-15)
Goal-oriented adaptivity is a powerful tool to accurately approximate physically relevant solution features for partial differential equations. In time dependent problems, we seek to represent the error in the quantity of ...
• Normal lubrication force between spherical particles immersed in a shear-thickening fluid ﻿

(Physics of Fluids, 2018-12-07)
In this work, the inverse bi-viscous model [Physics of Fluids 29, 103104 (2017)] is used to describe a shear-thickening fluid. An analytical velocity profile in a planar Poiseuille flow is utilized to calculate an approximate ...
• Apparent slip mechanism between two spheres based on solvent rheology: Theory and implication for the shear thinning of non-Brownian suspensions ﻿

(Physical Review Fluids, 2018-12-10)
Analytical results for the apparent slip between two spheres in a simple biviscous model of a shear thinning fluid are presented. Velocity profiles and apparent slip lengths along the surfaces are analyzed in order to ...
• Source time reversal (STR) method for linear elasticity ﻿

(Computers & Mathematics with Applications, 2018)
We study the problem of source reconstruction for a linear elasticity problem applied to seismicity induced by mining. We assume the source is written as a variable separable function $\mathbf{f(x)}\>g(t)$ . We first present ...
• Nonlinear computations of heave motions for a generic Wave Energy Converter ﻿

(In Vittorio Bucci Alberto Marinò (Eds.), Technology and Science for the Ships of the Future, Proceedings of NAV 2018: 19th International Conference on Ship and Maritime Research, IOS Press BV, 2018)
A bench-marking activity of numerical methods for analysis of Wave Energy Converters (WEC) was proposed under the Ocean Energy Systems (OES) International Energy Agency (IEA) Task 10 in 2015. The purpose of the benchmark ...
• Finite Element Simulations of Two-phase Flow and Floating Bodies Using FEniCS-HPC ﻿

(13th World Congress in Computational Mechanics WCCM, New York, USA, 2018-07)
We present a variational multiscale stabilized finite element method to solve the variable density incompressible Navier-Stokes equations for the simulation of two-phase flow. We introduce a level-set method based on the ...
• Adaptive Direct FEM Simulation with Unicorn/FEniCS-HPC for CS1 ﻿

(5th International Workshop on High Order CFD Methods, 2018-01-01)
• Fast One-dimensional Finite Element Approximation of Geophysical Measurements ﻿

(2018)
There exist a wide variety of geophysical prospection methods. In this work, we focus on resistivity methods. We categorize these resistivity prospection methods according to their acquisition location as (a) on the surface, ...
• Gaussian quadrature for $C^1$ cubic Clough-Tocher macro-triangles ﻿

(Journal of Computational and Applied Mathematics, 2018-10-31)
A numerical integration rule for multivariate cubic polynomials over n-dimensional simplices was designed by Hammer and Stroud [14]. The quadrature rule requires n + 2 quadrature points: the barycentre of the simplex and ...
• Generalization of the Pythagorean Eigenvalue Error Theorem and its Application to Isogeometric Analysis ﻿

(Numerical Methods for PDEs, 2018-10-13)
This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagation and structural vibration problems. The dispersion error of the isogeometric elements is minimized by optimally blending ...
• International energy agency ocean energy systems task 10 wave energy converter modeling verification and validation ﻿

(Proceedings of European Wave and Tidal Energy Conference, 2017)
This is the first joint reference paper for the Ocean Energy Systems (OES) Task 10 Wave Energy Converter modeling verification and validation group. The group is established under the OES Energy Technology Network program ...
• A partition of unity finite element method for computational diffusion MRI ﻿

(Journal of Computational Physics, 2018)
The Bloch–Torrey equation describes the evolution of the spin (usually water proton) magnetization under the influence of applied magnetic field gradients and is commonly used in numerical simulations for diffusion MRI ...
• Simulation of the HarshLab floating platform for offshore experimentation using FEniCS-HPC ﻿

(Poster EUSKAMPUS IV Marine Energy Conference, 2017)
• Direct finite element simulation of turbulent flow for marine based renewable energy ﻿

(Companion paper to F. Wendt, et. al. International energy agency ocean energy systems task 10 wave energy converter modeling verification and validation. In 12th European Wave and Tidal Energy Conference, 2017., 2017)
In this article we present a computational framework for simulation of turbulent flow in marine based renewable energy applications. In particular, we focus on floating structures and rotating turbines. This work is an ...
• A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements ﻿

(Geosciences, 2018-06-14)
In some geological formations, borehole resistivity measurements can be simulated using a sequence of 1D models. By considering a 1D layered media, we can reduce the dimensionality of the problem from 3D to 1.5D via a ...
• Numerical simulation of the von Kármán sodium dynamo experiment ﻿

(Journal of Fluid Mechanics, 2018-09-03)
We present hydrodynamic and magnetohydrodynamic (MHD) simulations of liquid sodium flows in the von Kármán sodium (VKS) set-up. The counter-rotating impellers made of soft iron that were used in the successful 2006 experiment ...
• Goal-oriented adaptivity using unconventional error representations for the multi-dimensional Helmholtz equation ﻿

(International Journal for Numerical Methods in Engineering, 2017-06-27)
In goal‐oriented adaptivity, the error in the quantity of interest is represented using the error functions of the direct and adjoint problems. This error representation is subsequently bounded above by element‐wise error ...
• Refined Isogeometric Analysis for a Preconditioned Conjugate Gradient Solver ﻿

(Computer Methods in Applied Mechanics and Engineering, 2018-06-15)
Starting from a highly continuous Isogeometric Analysis (IGA) discretization, refined Isogeometric Analysis (rIGA) introduces $C^0$ hyperplanes that act as separators for the direct LU factorization solver. As a result, ...
• On numerical quadrature for $C^1$ quadratic Powell-Sabin 6-split macro-triangles ﻿

(Journal of Computational and Applied Mathematics, 2018-08-01)
The quadrature rule of Hammer and Stroud [16] for cubic polynomials has been shown to be exact for a larger space of functions, namely the $C^1$ cubic Clough-Tocher spline space over a macro-triangle if and only if the ...
• Variational multiscale stabilization for compressible flow ﻿

(Computer Methods in Applied Mechanics and Engineering, 2018)
This paper presents a variational multiscale stabilization for the finite element numerical solution of the Euler and Navier-Stokes equations of compressible flow. All the components of the dual operator are considered in ...