673 research outputs found
An implicit-explicit solver for a two-fluid single-temperature model
We present an implicit-explicit finite volume scheme for two-fluid
single-temperature flow in all Mach number regimes which is based on a
symmetric hyperbolic thermodynamically compatible description of the fluid
flow. The scheme is stable for large time steps controlled by the interface
transport and is computational efficient due to a linear implicit character.
The latter is achieved by linearizing along constant reference states given by
the asymptotic analysis of the single-temperature model. Thus, the use of a
stiffly accurate IMEX Runge Kutta time integration and the centered treatment
of pressure based quantities provably guarantee the asymptotic preserving
property of the scheme for weakly compressible Euler equations with variable
volume fraction. The properties of the first and second order scheme are
validated by several numerical test cases
An interface capturing method for liquid-gas flows at low-Mach number
Multiphase, compressible and viscous flows are of crucial importance in a
wide range of scientific and engineering problems. Despite the large effort
paid in the last decades to develop accurate and efficient numerical techniques
to address this kind of problems, current models need to be further improved to
address realistic applications. In this context, we propose a numerical
approach to the simulation of multiphase, viscous flows where a compressible
and an incompressible phase interact in the low-Mach number regime. In this
frame, acoustics is neglected but large density variations of the compressible
phase can be accounted for as well as heat transfer, convection and diffusion
processes. The problem is addressed in a fully Eulerian framework exploiting a
low-Mach number asymptotic expansion of the Navier-Stokes equations. A Volume
of Fluid approach (VOF) is used to capture the liquid-gas interface, built on
top of a massive parallel solver, second order accurate both in time and space.
The second-order-pressure term is treated implicitly and the resulting pressure
equation is solved with the eigenexpansion method employing a robust and novel
formulation. We provide a detailed and complete description of the theoretical
approach together with information about the numerical technique and
implementation details. Results of benchmarking tests are provided for five
different test cases
Steady State Convergence Acceleration of the Generalized Lattice Boltzmann Equation with Forcing Term through Preconditioning
Several applications exist in which lattice Boltzmann methods (LBM) are used
to compute stationary states of fluid motions, particularly those driven or
modulated by external forces. Standard LBM, being explicit time-marching in
nature, requires a long time to attain steady state convergence, particularly
at low Mach numbers due to the disparity in characteristic speeds of
propagation of different quantities. In this paper, we present a preconditioned
generalized lattice Boltzmann equation (GLBE) with forcing term to accelerate
steady state convergence to flows driven by external forces. The use of
multiple relaxation times in the GLBE allows enhancement of the numerical
stability. Particular focus is given in preconditioning external forces, which
can be spatially and temporally dependent. In particular, correct forms of
moment-projections of source/forcing terms are derived such that they recover
preconditioned Navier-Stokes equations with non-uniform external forces. As an
illustration, we solve an extended system with a preconditioned lattice kinetic
equation for magnetic induction field at low magnetic Prandtl numbers, which
imposes Lorentz forces on the flow of conducting fluids. Computational studies,
particularly in three-dimensions, for canonical problems show that the number
of time steps needed to reach steady state is reduced by orders of magnitude
with preconditioning. In addition, the preconditioning approach resulted in
significantly improved stability characteristics when compared with the
corresponding single relaxation time formulation.Comment: 47 pages, 21 figures, for publication in Journal of Computational
Physic
On the discrete equation model for compressible multiphase fluid flows
The modeling of multi-phase flow is very challenging, given the range of
scales as well as the diversity of flow regimes that one encounters in this
context. We revisit the discrete equation method (DEM) for two-phase flow in
the absence of heat conduction and mass transfer. We analyze the resulting
probability coefficients and prove their local convexity, rigorously
establishing that our version of DEM can model different flow regimes ranging
from the disperse to stratified (or separated) flow. Moreover, we reformulate
the underlying mesoscopic model in terms of an one-parameter family of PDEs
that interpolates between different flow regimes. We also propose two sets of
procedures to enforce relaxation to equilibrium. We perform several numerical
tests to show the flexibility of the proposed formulation, as well as to
interpret different model components. The one-parameter family of PDEs provides
an unified framework for modeling mean quantities for a multiphase flow, while
at the same time identifying two key parameters that model the inherent
uncertainty in terms of the underlying microstructure
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