33 research outputs found
A Multiscale Diffuse-Interface Model for Two-Phase Flow in Porous Media
In this paper we consider a multiscale phase-field model for
capillarity-driven flows in porous media. The presented model constitutes a
reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model,
valid in situations where interest is restricted to dynamical and equilibrium
behavior in an aggregated sense, rather than a precise description of
microscale flow phenomena. The model is based on averaging of the equation of
motion, thereby yielding a significant reduction in the complexity of the
underlying Navier-Stokes-Cahn-Hilliard equations, while retaining its
macroscopic dynamical and equilibrium properties. Numerical results are
presented for the representative 2-dimensional capillary-rise problem
pertaining to two closely spaced vertical plates with both identical and
disparate wetting properties. Comparison with analytical solutions for these
test cases corroborates the accuracy of the presented multiscale model. In
addition, we present results for a capillary-rise problem with a non-trivial
geometry corresponding to a porous medium
Extension of a fast method for 2D steady free surface flow to stretched surface grids
Steady free surface flow is often encountered in marine engineering, e.g. for calculating ship hull resistance. When these flows are solved with CFD, the water-air interface can be represented using a surface fitting approach. The resulting free boundary problem requires an iterative technique to solve the flow and at the same time determine the free surface position. Most such methods use a time-stepping scheme, which is inefficient for solving steady flows. There is one steady technique which uses a special boundary condition at the free surface, but that method needs a dedicated coupled flow solver. To overcome these disadvantages an efficient free surface method was developed recently, in which the flow solver can be a black-box. It is based on quasi-Newton iterations which use a surrogate model in combination with flow solver inputs and outputs from previous iterations to approximate the Jacobian. As the original method was limited to uniform free surface grids, it is extended in this paper to stretched free surface grids. For this purpose, a different surrogate model is constructed by transforming a relation between perturbations of the free surface height and pressure from the wavenumber domain to the spatial domain using the convolution theorem. The method is tested on the 2D flow over an object. The quasi-Newton iterations converge exponentially and in a low number of iterations
Combining a least-squares approximate jacobian with an analytical model to couple a flow solver with free surface position updates
This paper presents a new quasi-Newton method suitable for systems that can be solved with a black-box solver for which a cheap surrogate model is available. In order to have fast convergence, the approximate Jacobian consists of two different contribution: a full rank surrogate model of the system is combined with a low rank least-squares model based on known input-output pairs of the system. It is then shown how this method can be used to solve 2D steady free surface flows with a black-box flow solver. The inviscid flow over a ramp is calculated for supercritical and subcritical conditions. For both simulations the quasi-Newton iterations converge exponentially and the results match the analytical predictions accurately
New techniques for solving the steady free surface flow problem
Steady free surface (FS) flows can be solved numerically with capturing or fitting methods, the latter being the subject of this paper. Most fitting methods are (pseudo-)transient and thus quite slow for steady flows; the so-called steady iterative method is much faster, but requires a dedicated solver because of the complex FS boundary conditions. The goal is to develop a (currently 2D) fitting method which is fast and can be used with a black box flow solver. Results from a perturbation analysis are used in combination with the IQN-ILS algorithm to construct such a method, applicable to supercritical flows. To tackle this method's scaling problem when the mesh is refined, an extension is proposed which uses a multigrid technique for the surface update. The flow over an object is simulated with the original and multigrid enhanced methods for three meshes. The multigrid method clearly outperforms the original one and is even mesh independent during part of its convergence.</p
Skeleton-stabilized ImmersoGeometric Analysis for incompressible viscous flow problems
A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for
incompressible viscous flow problems with moderate Reynolds number. The
proposed formulation fits within the framework of the finite cell method, where
essential boundary conditions are imposed weakly using a Nitsche-type method.
The key idea of the proposed formulation is to stabilize the jumps of
high-order derivatives of variables over the skeleton of the background mesh.
The formulation allows the use of identical finite-dimensional spaces for the
approximation of the pressure and velocity fields in immersed domains. The
stability issues observed for inf-sup stable discretizations of immersed
incompressible flow problems are avoided with this formulation. For B-spline
basis functions of degree with highest regularity, only the derivative of
order has to be controlled, which requires specification of only a single
stabilization parameter for the pressure field. The Stokes and Navier-Stokes
equations are studied numerically in two and three dimensions using various
immersed test cases. Oscillation-free solutions and high-order optimal
convergence rates can be obtained. The formulation is shown to be stable even
in limit cases where almost every elements of the physical domain is cut, and
hence it does not require the existence of interior cells. In terms of the
sparsity pattern, the algebraic system has a considerably smaller stencil than
counterpart approaches based on Lagrange basis functions. This important
property makes the proposed skeleton-stabilized technique computationally
practical. To demonstrate the stability and robustness of the method, we
perform a simulation of fluid flow through a porous medium, of which the
geometry is directly extracted from 3D scan data