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We consider the non-isothermal flow of a compressible fluid through pipes. Starting from the full set of Euler equations, we propose a variational characterization of solutions that encodes the conservation of mass, energy, and entropy in a…

Numerical Analysis · Mathematics 2016-11-11 Herbert Egger

In this work, we study the gradient discretisation method (GDM) of the time-dependent Navier-Stokes equations coupled with the heat equation, where the viscosity depends on the temperature. We design the discrete method and prove its…

Numerical Analysis · Mathematics 2024-11-25 Yahya Alnashri

We propose a finite element discretization for the steady, generalized Navier-Stokes equations for fluids with shear-dependent viscosity, completed with inhomogeneous Dirichlet boundary conditions and an inhomogeneous divergence constraint.…

Numerical Analysis · Mathematics 2023-10-09 Julius Jeßberger , Alex Kaltenbach

This article presents a new numerical scheme for the discretization of dissipative particle dynamics with conserved energy. The key idea is to reduce elementary pairwise stochastic dynamics (either fluctuation/dissipation or thermal…

Statistical Mechanics · Physics 2017-04-26 Gabriel Stoltz

We derive thermodynamically consistent models for diblock copolymer solutions coupled with the electric and magnetic field, respectively. These models satisfy the second law of thermodynamics and therefore are therefore thermodynamically…

Numerical Analysis · Mathematics 2021-03-30 Xiaowen Shen , Qi Wang

The paper introduces a finite element method for an Eulerian formulation of partial differential equations governing the transport and diffusion of a scalar quantity in a time-dependent domain. The method follows the idea from Lehrenfeld &…

Numerical Analysis · Mathematics 2025-06-26 Maxim Olshanskii , Henry von Wahl

In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn-Hilliard equations, Navier-Stokes equations and…

Numerical Analysis · Mathematics 2022-02-01 Xiaorong Wang , Xiaodi Zhang

In this note we describe a space-time boundary element discretization of the heat equation and an efficient and robust preconditioning strategy which is based on the use of boundary integral operators of opposite orders, but which requires…

Numerical Analysis · Mathematics 2018-11-14 Stefan Dohr , Olaf Steinbach

In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…

Numerical Analysis · Mathematics 2026-04-15 Xianping Li , Woinshet D. Mergia , Kailash C. Patidar

We present a new hydrodynamic model for incompressible binary fluids that is thermodynamically consistent and non-isothermal. This model follows the generalized Onsager principle and Boussinesq approximation and preserves the volume of each…

Fluid Dynamics · Physics 2023-08-14 Shouwen Sun , Liangliang Lei , Qi Wang

In this paper, we first establish a new fractional magnetohydrodynamic (MHD) coupled flow and heat transfer model for a generalized second-grade fluid. This coupled model consists of a fractional momentum equation and a heat conduction…

Numerical Analysis · Mathematics 2022-11-29 Xiaoqing Chi , Hui Zhang , Xiaoyun Jiang

In this paper, we propose a multiphysics finite element method for a quasi-static thermo-poroelasticity model with a nonlinear convective transport term. To design some stable numerical methods and reveal the multi-physical processes of…

Numerical Analysis · Mathematics 2023-10-10 Zhihao Ge , Dandan Xu

In the present work we propose and analyze a fully coupled virtual element method of high order for solving the two dimensional nonstationary Boussinesq system in terms of the stream-function and temperature fields. The discretization for…

Numerical Analysis · Mathematics 2023-03-22 L. Beirão da Veiga , D. Mora , A. Silgado

In this paper, we design and analyze a Virtual Element discretization for the steady motion of non-Newtonian, incompressible fluids. A specific stabilization, tailored to mimic the monotonicity and boundedness properties of the continuous…

Numerical Analysis · Mathematics 2024-03-07 P. F. Antonietti , L. Beirao da Veiga , M. Botti , G. Vacca , M. Verani

In the present contribution, we construct a virtual element (VE) discretization for the problem of miscible displacement of one incompressible fluid by another, described by a time-dependent coupled system of nonlinear partial differential…

Numerical Analysis · Mathematics 2019-07-31 Lourenco Beirao da Veiga , Alexander Pichler , Giuseppe Vacca

We develop a class of C1-continuous time integration methods that are applicable to conservative problems in elastodynamics. These methods are based on Hamilton's law of varying action. From the action of the continuous system we derive a…

Numerical Analysis · Mathematics 2016-04-18 Janine C. Mergel , Roger A. Sauer , Sina Ober-Blöbaum

We provide a fully nonlinear port-Hamiltonian formulation for discrete elastodynamical systems as well as a structure-preserving time discretization. The governing equations are obtained in a variational manner and represent index-1…

Dynamical Systems · Mathematics 2025-06-23 Philipp L. Kinon , Tobias Thoma , Peter Betsch , Paul Kotyczka

A novel numerical scheme including time and spatial discretization is offered for coupled Cahn-Hilliard and Navier-Stokes governing equation sys-tem in this paper. Variable densities and viscosities are considered in the nu-merical scheme.…

Computational Physics · Physics 2018-05-25 Xiaoyu Feng , Jisheng Kou , Shuyu Sun

In this paper, we develop a multiphysics finite element method for solving the quasi-static thermo-poroelasticity model with nonlinear permeability. The model involves multiple physical processes such as deformation, pressure, diffusion and…

Numerical Analysis · Mathematics 2026-02-24 Zhihao Ge , Wenshuai Hu

We present a structure-preserving discretization of the hybrid magnetohydrodynamics (MHD)-driftkinetic system for simulations of low-frequency wave-particle interactions. The model equations are derived from a variational principle,…

Computational Physics · Physics 2025-10-09 Byung Kyu Na , Stefan Possanner , Xin Wang