26 papers · ranked by Valyu relevance
Philip Cardiff, I. Demirdžić
Since early publications in the late 1980s and early 1990s, the finite volume method has been shown suitable for solid mechanics analyses. At present, there are several flavours of the method, including "cell-centred", "staggered", "vertex-centred", "periodic heterogenous microstructural", "Godunov-type"…
A. Aguayo-Ortiz, S. Mendoza, D. Olvera, Iratxe Puebla
In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the…
Richard A. Norton, Colin Fox, Malcolm E. K. Morrison
We develop a finite-dimensional approximation of the Frobenius-Perron operator using the finite volume method applied to the continuity equation for the evolution of probability. A Courant-Friedrichs-Lewy condition ensures that the approximation satisfies the Markov property, while existing convergence theory for the…
Roger Käppeli
We review well-balanced methods for the faithful approximation of solutions of systems of hyperbolic balance laws that are of interest to computational astrophysics. Well-balanced methods are specialized numerical techniques that guarantee the accurate resolution of non-trivial steady-state solutions, that balance laws…
Min-Ho Park, Aretha L. Teckentrup
We consider the application of multilevel Monte Carlo methods to steady state Darcy flow in a random porous medium, described mathematically by elliptic partial differential equations with random coefficients. The levels in the multilevel estimator are defined by finite volume discretisations of the governing equations…
Alexey Y. Chernyshenko, Maxim A. Olshanskii, Yuri Vassilevski
The paper develops a hybrid method for solving a system of advection–diffusion equations in a bulk domain coupled to advection–diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in the bulk is combined with a trace finite element method for equations posed on the…
Axel Henningsson, Stephen A. Hall, Maria Pia Morigi, Fauzia Albertin
A mathematical framework and accompanying numerical algorithm exploiting the continuity equation for 4D reconstruction of spatiotemporal attenuation fields from multi-angle full-field transmission measurements is presented. The algorithm is geared towards rotation-free dynamic multi-beam X-ray tomography measurements…
Johan Roenby, Henrik Bredmose, Hrvoje Jasak
We devise a numerical method for passive advection of a surface, such as the interface between two incompressible fluids, across a computational mesh. The method is called isoAdvector, and is developed for general meshes consisting of arbitrary polyhedral cells. The algorithm is based on the volume of fluid (VOF) idea…
Wade A. Walker, Jörg Langowski
In this paper we describe the repeated replacement method (RRM), a new meshfree method for computational fluid dynamics (CFD). RRM simulates fluid flow by modeling compressible fluids’ tendency to evolve towards a state of constant density, velocity, and pressure. To evolve a fluid flow simulation forward in time, RRM…
Vincenzo Gulizzi, Ann Almgren, John B. Bell
We present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an hp adaptive mesh…
Samuel H. Friedman, Ahmadreza Ghaffarizadeh, Paul Macklin
To simulate the spatiotemporal distribution of chemical compounds, we present BioFVM, an open-source reaction-diffusion equation solver using finite volume methods with motivation for biological applications. With various numerical solvers, we can simulate the interaction of dozens of compounds, including growth…
Céline Baranger, Nicolas Hérouard, Julien Mathiaud, Luc Mieussens
We present a numerical comparison between two standard finite volume schemes and a discontinuous Galerkin method applied to the BGK equation of rarefied gas dynamics. We pay a particular attention to the numerical boundary conditions in order to preserve the rate of convergence of the method. Most of our analysis…
Nicolas Castel, François-Xavier Coudert
Mechanical properties of amorphous phases of metal-organic frameworks, such as MOF glasses, are difficult to determine experimentally. Moreover, computational characterization is limited by the level of theory chosen for the description of interatomic interactions and is often computationally expensive. In this work…
José Luis Alonzo-Velázquez, Salvador Botello-Rionda, Rafael Herrera-Guzmán, Mauricio Carrillo-Tripp
Viruses are the most abundant pathogens affecting all forms of life. A major component of a virus is a protein shell, known as the viral capsid, that encapsulates the genomic material. The fundamental functions of the capsid are to protect and transport the viral genome, and recognize the host cell. Descriptions of…
Christopher T. Lee, Justin G. Laughlin, Nils Angliviel de La Beaumelle, Rommie E. Amaro + 4 more
Recent advances in electron microscopy have, for the first time, enabled imaging of single cells in 3D at a nanometer length scale resolution. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations will require a system for…
Asmus Ougaard Dohn, Verena Isabell Markmann, Amke Nimmrich, Kristoffer Haldrup + 2 more
Structural studies using x-ray scattering methods for investigating molecules in solution are shifting focus towards describing the role and effects of the surrounding solvent. However, forward models based on molecular dynamics (MD) simulations to simulate structure factors and x-ray scattering from interatomic…
Anotida Madzvamuse, David Hernandez–Aristizabal, Diego A. Garzon–Alvarado, Carlos A. Duque–Daza
Cell migration is an ubiquitous process in life that is mainly triggered by the dynamics of the actin cytoskeleton and therefore is driven by both mechanical properties and biochemical processes. It is a multistep process essential for mammalian organisms and is closely linked to development, cancer invasion and…
Göran Frenning
We describe a method to approximate the volume of Voronoi polyhedra in situations where recurring updates are needed for small changes in the geometry, as during simulations of confined compression of granular materials with the discrete element method (DEM) (see section ‘Additional information: background’). The…
Yue Mei, Jiahao Liu, Xu Guo, Brandon Zimmerman + 2 more
This paper presents a method to derive the virtual fields for identifying constitutive model parameters using the Virtual Fields Method (VFM). The VFM is an approach to identify unknown constitutive parameters using deformation fields measured across a given volume of interest. The general principle for solving…
Nils Edvin Richard Zimmermann, Gabriela Guevara-Carrion, Jadran Vrabec, Niels Hansen
The thermodiffusion behavior of binary Lennard-Jones mixtures in the liquid state was investigated by combining the individual strengths of non-equilibrium molecular dynamics (NEMD) and equilibrium molecular dynamics (EMD) simulations. On the one hand, boundarydriven NEMD simulations are useful to quickly predict Soret…
Morteza Roostaei, Alireza Nouri, Vahidoddin Fattahpour, Dave Chan
In petroleum engineering, the transport phenomenon of proppants in a fracture caused by hydraulic fracturing is captured by hyperbolic partial differential equations (PDEs). The solution of this kind of PDEs may encounter smooth transitions, or there can be large gradients of the field variables. The numerical…
Slobodan Milovanović, Lina von Sydow
In this paper, we consider the numerical pricing of financial derivatives using Radial Basis Function generated Finite Differences in space. Such discretization methods have the advantage of not requiring Cartesian grids. Instead, the nodes can be placed with higher density in areas where there is a need for higher…
Nicolas Castel, Dune André, Connor Edwards, Jack D. Evans + 1 more
The detailed understanding of the microscopic structure of amorphous phases of metal-organic frameworks (MOFs) remains a widely open question: characterization of these systems is very difficult, both from the experimental and computational point of view. In molecular simulations, approaches have been proposed that…
Sandor Balog, Barbara Rothen-Rutishauser, Alke Petri-Fink
Understanding the mechanisms of interaction between cells and particulate nanomaterials lies in the heart of assessing the hazard associated with nanoparticles. The paradigm of toxicology requires quantifying and interpreting dose-response relationships, and cells cultured in vitro and exposed to particle dispersions…
Authors not listed
We develop a highly parallelizable algorithm to calculate long-range electrostatic interactions named the Gauss-Legendre-Spherical-t (GLST) cubature method. Motivated by our recent spherical grid and treecode method, we utilize the Gauss-Legendre quadrature for integration over a finite range and spherical t-design for…
Michele Nottoli, Michael F. Herbst, Aleksandr Mikhalev, Abhinav Jha + 2 more
Polarizable continuum solvation models are popular in both, quantum chemistry and in biophysics, though typically with different requirements for the numerical methods. However, the recent trend of multiscale modeling can be expected to blur field-specific differences. In this regard, numerical methods based on domain…