Article
Engineering, Multidisciplinary
Manuel A. Sanchez, Bernardo Cockburn, Ngoc-Cuong Nguyen, Jaime Peraire
Summary: This paper presents a class of high-order finite element methods that conserve linear and angular momenta as well as energy for equations of linear elastodynamics by exploiting and preserving the Hamiltonian structure. Experimental results confirm optimal convergence and conservation properties of these methods.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Christoph Lehrenfeld, Paul Stocker
Summary: A new variant called embedded Trefftz discontinuous Galerkin method is proposed, which is the Galerkin projection of an underlying discontinuous Galerkin method onto a subspace of Trefftz-type. This method allows for convenient extension to general cases, reduces globally coupled unknowns significantly, and improves accuracy in the Helmholtz problem.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Mathematics, Applied
Ivy Weber, Gunilla Kreiss, Murtazo Nazarov
Summary: This paper investigates the stability of a numerical method for solving the wave equation using matrix eigenvalue analysis to calculate time-step restrictions. It is found that the time-step restriction for continuous Lagrange elements is independent of the nodal distribution, while the restriction for symmetric interior penalty DG schemes is tighter. The best time-step restriction is obtained for continuous Hermite finite elements.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Constantin Bacuta, Leszek Demkowicz, Jaime Mora, Christos Xenophontos
Summary: This work focuses on two problems: analyzing the DPG method in fractional energy spaces, and investigating a non-conforming version of the DPG method for general polyhedral meshes. The ultraweak variational formulation is used for the model Laplace equation, and theoretical estimates are supported by 3D numerical experiments.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Ngoc Cuong Nguyen, Jordi Vila-Perez, Jaime Peraire
Summary: This article introduces an adaptive viscosity regularization approach for solving systems of nonlinear conservation laws with shock waves. The approach combines regularization and mesh adaptation strategies to reduce artificial dissipation and improve shock capturing accuracy.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
R. C. Moura, L. D. Fernandes, A. F. C. Silva, G. Mengaldo, S. J. Sherwin
Summary: In recent years, dispersion-diffusion (eigen)analyses have been used to evaluate the accuracy and stability of spectral element methods (SEMs) for under-resolved computations of transitional and turbulent flows. This study unveils a linear mechanism that causes energy transfer across Fourier modes in SEM computations and highlights the potential improvement of dissipation estimation by considering this mechanism in eigenanalysis.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
T. Dzanic, F. D. Witherden
Summary: This work presents a positivity-preserving entropy-based adaptive filtering method for shock capturing in discontinuous spectral element methods. The method adapts the filter strength to enforce positivity and a local discrete minimum entropy principle, allowing it to robustly handle strong discontinuities with sub-element resolution. It does not require problem-dependent parameter tuning and can be easily implemented on general unstructured meshes with relatively low computational cost.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Engineering, Multidisciplinary
Manuel A. Sanchez, Shukai Du, Bernardo Cockburn, Ngoc-Cuong Nguyen, Jaime Peraire
Summary: In this paper, several high-order accurate finite element methods for the Maxwell's equations are presented, which provide time-invariant, non-drifting approximations to the total electric and magnetic charges, and to the total energy. These methods are devised by taking advantage of the Hamiltonian structures of the Maxwell's equations and using spatial and temporal discretization techniques to ensure the conservation properties and convergence of the methods.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Shukai Du, Samuel N. Stechmann
Summary: This article presents a numerical method for efficient and low-memory calculations of the radiative transfer equation. The method reduces the number of spatial degrees of freedom and utilizes a suitable preconditioner to ensure a computational cost of O(N). Numerical examples demonstrate the effectiveness of the method in reducing memory requirements and computational cost.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
C. Engstrom, S. Giani, L. Grubisic
Summary: This paper introduces the application and performance comparison of discontinuous Galerkin composite finite element methods (DGCFEM) in addressing approximation problems on complicated domains.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Tale Bakken Ulfsby, Andre Massing, Simon Sticko
Summary: We propose a novel cut discontinuous Galerkin (CutDG) method for solving stationary advection-reaction problems on surfaces embedded in Rd. The approach involves embedding the surface into a full-dimensional background mesh and using discontinuous piecewise polynomials as test and trial functions. By introducing a suitable stabilization technique, we are able to establish inf-sup stability, a priori error estimates, and condition number estimates using an augmented streamline-diffusion norm. Numerical examples validate our theoretical findings.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Applied
Zhiqiang Cai, Jing Yang
Summary: In this paper, a class of discontinuous Galerkin finite element methods for advection-diffusion-reaction problems is presented, and a priori error estimates are established when the solution is only in H1+s (Omega) space with s is an element of(0, 1/2].
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Scott Congreve, Paul Houston
Summary: This article considers the extension of two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of second-order quasilinear elliptic boundary value problems of monotone type to the case when agglomerated polygonal/polyhedral meshes are employed for the coarse mesh approximation. By extending the existing error analysis and developing an hp-adaptive two-grid algorithm, the fine and coarse finite element spaces can be adaptively designed in an automatic manner. Numerical experiments demonstrate the computational performance of the proposed method.
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2022)
Article
Mathematics, Applied
David A. Kopriva, Gregor J. Gassner, Jan Nordstrom
Summary: The paper discusses using the behavior of the L-2 norm to infer stability of discontinuous Galerkin spectral element methods for linear hyperbolic equations. By utilizing an upwind numerical flux that satisfies the Rankine-Hugoniot condition, the DGSEM is shown to have the same energy bound in the L-2 norm as the partial differential equation, with added dissipation depending on the approximation error.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Computer Science, Interdisciplinary Applications
Andres M. Rueda-Ramirez, Will Pazner, Gregor J. Gassner
Summary: This paper presents a general family of subcell limiting strategies for constructing robust high-order accurate nodal discontinuous Galerkin schemes. The main strategy is to combine compatible low order finite volume discretizations with high-order variants to guarantee additional properties such as bounds on physical quantities and guaranteed entropy dissipation. The resulting methods can be used on unstructured curvilinear meshes, handle strong shocks efficiently, and guarantee physical bounds on quantities such as density, pressure, or entropy.
COMPUTERS & FLUIDS
(2022)
Editorial Material
Mechanics
Guillaume Houzeaux, Marta Garcia-Gasulla
INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS
(2020)
Article
Nuclear Science & Technology
Alejandro Soba, Mauricio E. Cazado, Guillaume Houzeaux, Albert Gutierrez-Milla, Mervi J. Mantsinen, Xavier Saez
Summary: The study presents significant improvements and validations of a deterministic neutron transport code dedicated to solving the Boltzmann Transport Equation. The code is integrated as a module in the Alya software package using multi-group energy discretization and FEM on unstructured meshes to treat complex domains. Real base expressions are used to introduce the anisotropy of the scattering medium.
FUSION ENGINEERING AND DESIGN
(2021)
Article
Engineering, Mechanical
C. Samaniego, J. Ulloa, P. Rodriguez, G. Houzeaux, M. Vazquez, E. Samaniego
Summary: This study contributes to the understanding of localized failure mechanisms using phase fields in a variational framework. It introduces a new degradation function to distinguish between plastic strain localization and ductile fracture mechanisms, and proposes a parallel implementation of the phase-field approach to tackle potential high computational costs. Several examples demonstrate the capabilities of this implementation in capturing different failure mechanisms.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2021)
Article
Mechanics
J. C. Cajas, D. Pastrana, I Rodriguez, O. Lehmkuhl, G. Houzeaux, M. Vazquez, C. Trevino
Summary: In this study, vortex induced vibrations of a pivoted cylinder with finite height were numerically investigated using a mathematical model. Various parameters were considered and results on solid body trajectories, amplitude of oscillations, hydrodynamic force coefficients, wake structure, and details on vortex shedding near the cylinder were presented. The numerical results showed good agreement with established VIV systems, suggesting potential for future research in related VIV systems at larger Reynolds numbers.
Article
Mechanics
Hadrien Calmet, Kiao Inthavong, Ambrus Both, Anurag Surapaneni, Daniel Mira, Beatriz Egukitza, Guillaume Houzeaux
Summary: This study used high-fidelity simulations to predict the dispersion of droplets produced by coughing, showing that droplets with small diameters mainly contribute to the risk of respiratory transmission.
Article
Biochemical Research Methods
Alfonso Santiago, Constantine Butakoff, Beatriz Eguzkitza, Richard A. Gray, Karen May-Newman, Pras Pathmanathan, Vi Vu, Mariano Vazquez
Summary: This study presents a model of the LV-LVAD system and a VVUQ plan based on ASME standards to ensure credible predictions. The simulation was validated using the SDSU cardiac simulator, and the numerical model was based on Alya. The VVUQ plan included risk analysis, verification stage, sensitivity analysis, and uncertainty quantification. The results showed correctness of the solution procedure and identified the most impactful inputs for the analysed quantities of interest. The simulations were computationally expensive but demonstrated the feasibility of stringent VVUQ according to ASME standards.
PLOS COMPUTATIONAL BIOLOGY
(2022)
Article
Computer Science, Interdisciplinary Applications
G. Houzeaux, R. M. Badia, R. Borrell, D. Dosimont, J. Ejarque, M. Garcia-Gasulla, V Lopez
Summary: This work presents an elastic computing methodology that adjusts the allocated resources to a simulation automatically based on the runtime measure of communication efficiency, resulting in efficient simulations.
COMPUTERS & FLUIDS
(2022)
Article
Engineering, Civil
Abhishek Mukherjee, Juan Carlos Cajas, Guillaume Houzeaux, Oriol Lehmkuhl, Jenny Suckale, Simone Marras
Summary: This study investigates the impact of rigidity and vegetation density on energy reflection and dissipation in coastal forests using a three-dimensional computational fluid dynamics model. The results reveal that the blockage area created by multiple tree trunks, rather than rigidity, plays a dominant role in energy reflection. The presence of trees alters the flow field, causing turbulent kinetic energy generation and flow energy dissipation. Therefore, coastal forests reduce the onshore energy flux of tsunamis through both reflection and dissipation.
COASTAL ENGINEERING
(2023)
Article
Pharmacology & Pharmacy
Hadrien Calmet, Damien Dosimont, David Oks, Guillaume Houzeaux, Brenda Vara Almirall, Kiao Inthavong
Summary: Targeted nasal drug delivery can be improved by adjusting spray parameters. This study investigated the effects of different values of six spray parameters on particle deposition. Sensitivity analysis showed that particle size significantly affected deposition in the olfactory and posterior regions, while spray device insertion angle had a significant impact on deposition in the anterior and middle regions. Machine learning models based on 384 cases provided accurate predictions despite the small sample dataset.
INTERNATIONAL JOURNAL OF PHARMACEUTICS
(2023)
Article
Engineering, Marine
Ruixue Liu, Cosan Daskiran, Abhishek Mukherjee, Qin Xin, Fangda Cui, Simone Marras, Hena Farooqi, Heather Dettman, Michel Boufadel
Summary: A mesoscale oil spill test tank was used to study the mixing energy and particle behavior near the shorelines. Different types of waves were generated and their velocities and energy dissipation rates were measured. Large-Eddy Simulation (LES) was conducted to further analyze the particle movement under typical wave conditions. The results showed that droplet inertia had a significant impact on particle accumulation.
Article
Mechanics
J. C. Cajas, I. Rodriguez, E. Salcedo, O. Lehmkuhl, G. Houzeaux, C. Trevino
Summary: The effect of aspect ratio on vortex induced vibrations (VIV) of a pivoted circular cylinder with different length-to-diameter ratios was studied. The study found that the aspect ratio influenced the oscillation amplitudes, synchronization region, and wake structures. At lower reduced velocities, steady symmetrical flow was obtained for cylinders with small aspect ratios, but became unstable at higher velocities.
Article
Computer Science, Interdisciplinary Applications
David Oks, Guillaume Houzeaux, Mariano Vazquez, Michael Neidlin, Cristobal Samaniego
Summary: This study evaluates the effect of TAVR commissural alignment on coronary perfusion and device performance using a computational fluid-structure interaction model.
COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE
(2023)
Article
Energy & Fuels
Abel Gargallo-Peiro, Gonzalo Revilla, Matias Avila, Guillaume Houzeaux
Summary: A novel approach for wind farm simulation is presented, featuring realignment and mesh adaptation. The method utilizes actuator discs to model turbines and combines a level-set-based simulation framework with an adaptation cycle. The results demonstrate the accuracy and efficiency of the proposed approach in simulating complex wind farm configurations.
Review
Geosciences, Multidisciplinary
Simone Marras, Kyle T. Mandli
Summary: In recent years, tsunami modeling and simulation techniques have undergone significant changes, driven by exa-scale computing and hybrid computing. Different approaches to tsunami simulation have limitations based on flow states, and there are still challenges to overcome in achieving a comprehensive multi-scale modeling infrastructure.
Article
Computer Science, Interdisciplinary Applications
H. Calmet, K. Inthavong, H. Owen, D. Dosimont, O. Lehmkuhl, G. Houzeaux, M. Vazquez
Summary: CFD has shown great potential as a diagnostic tool in clinical trials, but overall statistical findings from large population samples are necessary for real clinical applications. This study compared a highly-resolved solution with lower resolution models to determine minimum modelling criteria for accurate respiratory flows in large-scale clinical applications. Results indicated that lower resolution models could achieve sufficient accuracy if mean flow was considered, and a stable transient result required data at least from the second respiration cycle. The study's findings offer guidance for future modelling efforts in clinical and engineering applications.
COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING
(2021)