Related papers: A Numerical Scheme for Non-Newtonian Fluids and Pl…
A new second-order numerical scheme based on an operator splitting is proposed for the Godunov-Peshkov-Romenski model of continuum mechanics. The homogeneous part of the system is solved with a finite volume method based on a WENO…
This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics proposed by Peshkov & Romenski (HPR model), which is based on the theory of nonlinear hyperelasticity of Godunov &…
We present a new hybrid semi-implicit finite volume / finite element numerical scheme for the solution of incompressible and weakly compressible media. From the continuum mechanics model proposed by Godunov, Peshkov and Romenski (GPR), we…
We are concerned with the numerical solution of a unified first order hyperbolic formulation of continuum mechanics that originates from the work of Godunov, Peshkov and Romenski (GPR model) and which is an extension of nonlinear…
This chapter deals with multi-material flow problems by a kind of effective numerical methods, based on a series of reduced forms of the Baer-Nunziato (BN) model. Numerical simulations often face a host of difficult challenges, typically…
We present a numerical method to model the dynamics of inextensible biomembranes in a quasi-Newtonian incompressible flow, which better describes hemorheology in the small vasculature. We consider a level set model for the fluid-membrane…
In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realized in the semi-discrete finite-volume framework and is based…
In recent years, non-Newtonian fluids have received much attention due to their numerous applications, such as plastic manufacture and extrusion of polymer fluids. They are more complex than Newtonian fluids because the relationship between…
We discuss the applicability of a unified hyperbolic model for continuum fluid and solid mechanics to modeling non-Newtonian flows and in particular to modeling the stress-driven solid-fluid transformations in flows of viscoplastic fluids,…
In this paper, we propose a new unified first order hyperbolic model of Newtonian continuum mechanics coupled with electro-dynamics. The model is able to describe the behavior of moving elasto-plastic dielectric solids as well as viscous…
A numerical method is developed for solving a system of partial differential equations modeling the flow of a nematic liquid crystal fluid with stretching effect, which takes into account the geometrical shape of its molecules. This system…
In this work, we suggest an easy-to-code higher-order finite volume semi-discrete scheme to analyze the nonlinear behavior of the electron-plasma oscillations by solving electron fluid equations numerically. The present method employs a…
Machine learning techniques are being used as an alternative to traditional numerical discretization methods for solving hyperbolic partial differential equations (PDEs) relevant to fluid flow. Whilst numerical methods are higher fidelity,…
This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov & Romenski, denoted as HPR model. In that framework, the viscous stresses are computed…
The space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting was used for simulation of multidimensional reacting flows with detonation waves. The presented numerical…
In this work, we design and analyze a Hybrid High-Order (HHO) discretization method for incompressible flows of non-Newtonian fluids with power-like convective behaviour. We work under general assumptions on the viscosity and convection…
We describe a newly developed cosmological hydrodynamics code based on the weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws. High order finite difference WENO schemes are designed for problems with…
Nonlocal material response distinctively changes the optical properties of nano-plasmonic scatterers and waveguides. It is described by the nonlocal hydrodynamic Drude model, which -- in frequency domain -- is given by a coupled system of…
We present a new multidimensional classical hydrodynamics code based on Semidiscrete Central Godunov-type schemes and high order Weighted Essentially Non-oscillatory (WENO) data reconstruction. This approach is a lot simpler and easier to…
In [1], the non-linear space-time Hasegawa-Mima plasma equation is formulated as a coupled system of two linear PDE's, a solution of which is a pair (u, w). The first equation is of hyperbolic type and the second of elliptic type.…