Versatile Mixed Methods for Non-Isothermal Incompressible Flows

一种准确的有限元方法用于粘性流体等温不可压缩流动的数值求解

An accurate finite element method for the numerical solution of isothermal and incompressible flow of viscous fluid

本文提出了一种无需稳定化或分裂方案的通用方法，用于求解粘性流体流动问题，通过平衡方程直接求解，提高了计算的准确性和鲁棒性，适用于多物理场应用。

Versatile Mixed Methods for the Incompressible Navier-Stokes Equations

In the spirit of the "Principle of Equipresence" introduced by Truesdell & Toupin, The Classical Field Theories (1960), we use the full version of the viscous stress tensor which was originally derived for compressible flows, instead of the classical incompressible stress tensor. In our approach, the divergence-free constraint for the viscous stress term is not enforced ahead of discretization. Instead, our formulation allows the scheme itself to "choose" a consistent way to interpret the divergence-free constraint: i.e., the divergence-free constraint is interpreted (or enforced) in a consist…

varRhoTurbVOF: a new set of volume of fluid solvers for turbulent isothermal multiphase flows in OpenFOAM

The volume of fluid (VOF) method is a popular approach for multiphase flow modeling. The open-source computational fluid dynamics (CFD) software, OpenFOAM, implements a variety of VOF-based solvers and provides users a wide range of turbulence models. Since isothermal multiphase flows under the VOF framework belong to the variable-density incompressible flow category, the isothermal VOF-based solvers in OpenFOAM fail to use the correct turbulence models. varRhoTurbVOF is designed to solve this issue and with the hope to replace all the corresponding existing solvers in the future. With the obj…

A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem

A novel notion for constructing a well-balanced scheme - a gradient-robust scheme - is introduced and a showcase application for a steady compressible, isothermal Stokes equations is presented. Gradient-robustness means that arbitrary gradient fields in the momentum balance are well-balanced by the discrete pressure gradient - if there is enough mass in the system to compensate the force. The scheme is asymptotic-preserving in the sense that it degenerates for low Mach numbers to a recent inf-sup stable and pressure-robust discretization for the incompressible Stokes equations. The convergence…

Conservative finite-volume framework and pressure-based algorithm for flows of incompressible, ideal-gas and real-gas fluids at all speeds

A conservative finite-volume framework, based on a collocated variable arrangement, for the simulation of flows at all speeds, applicable to incompressible, ideal-gas and real-gas fluids is proposed in conjunction with a fully-coupled pressure-based algorithm. The applied conservative discretisation and implementation of the governing conservation laws as well as the definition of the fluxes using a momentum-weighted interpolation are identical for incompressible and compressible fluids, and are suitable for complex geometries represented by unstructured meshes. Incompressible fluids are descr…

General and exact pressure evolution equation

A crucial issue in fluid dynamics is related to the knowledge of the fluid pressure. A new general pressure equation is derived from compressible Navier-Stokes equation. It is argued that this new pressure equation allows unifying compressible, low-Mach and incompressible approaches. Moreover, this equation should be able to replace the Poisson equation in isothermal incompressible fluids. For computational fluid dynamics, it can be seen as an alternative to Lattice Boltzmann methods and as the physical justification of artificial com-pressibility.