52 research outputs found
An accelerated sharp-interface method for multiphase flows simulations
In this work, we develop an accelerated sharp-interface method based on (Hu
et al., JCP, 2006) and (Luo et al., JCP, 2015) for multiphase flows
simulations. Traditional multiphase simulation methods use the minimum time
step of all fluids obtained according to CFL conditions to evolve the fluid
states, which limits the computational efficiency, as the sound speed c of one
fluid may be much larger than the others. To address this issue, based on the
original GFM-like sharp interface methods, the present method is developed by
solving the governing equations of each individual fluid with the corresponding
time step. Without violating the numerical stability requirement, the states of
fluid with larger time-scale features will be updated with a larger time step.
The interaction step between two fluids is solved for synchronization, which is
handled by interpolating the intermediate states of fluid with larger
time-scale features. In addition, an interfacial flux correction is implemented
to maintain the conservative property. The present method can be combined with
a wavelet-based adaptive multi-resolution algorithm (Han et al., JCP, 2014) to
achieve additional computational efficiency. A number of numerical tests
indicate that the accuracy of the results obtained by the present method is
comparable to the original costly method, with a significant speedup
A variational-level-set based partitioning method for block-structured meshes
We propose a numerical method for solving block-structured mesh partitioning
problems based on the variational level-set method of (Zhao et al., J Comput
Phys 127, 1996) which has been widely used in many partitioning problems such
as image segmentation and shape optimization. Here, the variational model and
its level-set formulation have been simplified that only one single level-set
function is evolved. Thus, the numerical implementation becomes simple, and the
computational and memory overhead are significantly alleviated, making this
method suitable for solving realistic block-structured mesh partitioning
problems where a large number of regions is required. We start to verify this
method by a range of two-dimensional and three-dimensional uniform mesh
partitioning cases. The results agree with the theoretical solutions very well
and converge rapidly. More complex cases, including block-structured adaptive
mesh partitioning for single-phase and multi-phase multi-resolution
simulations, confirm the accuracy, robustness and good convergence property.
The measured CPU time shows that this method is efficient for both
two-dimensional and three-dimensional realistic partitioning problems in
parallel computing. The proposed method has the potential to be extended to
solve other partitioning problems by replacing the energy functional
A consistent analytical formulation for volume-estimation of geometries enclosed by implicitly defined surfaces
We have derived an analytical formulation for estimating the volume of
geometries enclosed by implicitly defined surfaces. The novelty of this work is
due to two aspects. First we provide a general analytical formulation for all
two-dimensional cases, and for elementary three three-dimensional cases by
which the volume of general three-dimensional cases can be computed. Second,
our method addresses the inconsistency issue due to mesh refinement. It is
demonstrated by several two-dimensional and three-dimensional cases that this
analytical formulation exhibits 2nd-order accuracy
A network partition method for solving large-scale complex nonlinear processes
A numerical framework based on network partition and operator splitting is
developed to solve nonlinear differential equations of large-scale dynamic
processes encountered in physics, chemistry and biology. Under the assumption
that those dynamic processes can be characterized by sparse networks, we
minimize the number of splitting for constructing subproblems by network
partition. Then the numerical simulation of the original system is simplified
by solving a small number of subproblems, with each containing uncorrelated
elementary processes. In this way, numerical difficulties of conventional
methods encountered in large-scale systems such as numerical instability,
negative solutions, and convergence issue are avoided. In addition, parallel
simulations for each subproblem can be achieved, which is beneficial for
large-scale systems. Examples with complex underlying nonlinear processes,
including chemical reactions and reaction-diffusion on networks, demonstrate
that this method generates convergent solution in a efficient and robust way
A conservative sharp-interface method for compressible multi-material flows
In this paper we develop a conservative sharp-interface method dedicated to
simulating multiple compressible fluids. Numerical treatments for a cut cell
shared by more than two materials are proposed. First, we simplify the
interface interaction inside such a cell with a reduced model to avoid explicit
interface reconstruction and complex flux calculation. Second, conservation is
strictly preserved by an efficient conservation correction procedure for the
cut cell. To improve the robustness, a multi-material scale separation model is
developed to consistently remove non-resolved interface scales. In addition,
the multi-resolution method and local time-stepping scheme are incorporated
into the proposed multi-material method to speed up the high-resolution
simulations. Various numerical test cases, including the multi-material shock
tube problem, inertial confinement fusion implosion, triple-point shock
interaction and shock interaction with multi-material bubbles, show that the
method is suitable for a wide range of complex compressible multi-material
flows
A Split Random Time Stepping Method for Stiff and Non-stiff Chemically Reacting Flows
In this paper, a new fractional step method is proposed for simulating stiff
and nonstiff chemically reacting flows. In stiff cases, a well-known spurious
numerical phenomenon, i.e. the incorrect propagation speed of discontinuities,
may be produced by general fractional step methods due to the under-resolved
discretization in both space and time. The previous random projection method
has been successfully applied for stiff detonation capturing in under-resolved
conditions. Not to randomly project the intermediate state into two presumed
equilibrium states (completely burnt or unburnt) as in the random projection
method, the present study is to randomly choose the time-dependent advance or
stop of a reaction process. Each one-way reaction has been decoupled from the
multi-reaction kinetics using operator splitting and the local smeared
temperature due to numerical dissipation of shock-capturing schemes is compared
with a random one within two limited temperatures corresponding to the advance
and its inverse states, respectively, to control the random reaction. The
random activation or deactivation in the reaction step is thus promising to
correct the deterministic accumulative error of the propagation of
discontinuities. Extensive numerical experiments, including model problems and
realistic reacting flows in one and two dimensions, demonstrate this
expectation as well as the effectiveness and robustness of the method.
Meanwhile, for nonstiff problems when spatial and temporal resolutions are
fine, the proposed random method recovers the results as general fractional
step methods, owing to the increasing possibility of activation with
diminishing randomness by adding a shift term.Comment: 48 pages, 14 figure
Finite volume based film flow and ice accretion models on aircraft wings
The thin runback water films driven by the gas flow, the pressure gradient
and the gravity on the iced aircraft surface are investigated in this paper. A
three-dimensional film flow model based on Finite Volume Method (FVM) and the
lubrication theory is proposed to describe the flow. The depth-averaged
velocity of the film is stored in Cartesian coordinates to avoid the appearance
of the metric tensors. The governing equations are discretized in the first
layer structured grid cell which is selected as the grids for film flow. In
order to verify this method, comparisons between numerical results and
experimental results of ice shapes on NACA 0012 airfoil and GLC-305 swept wing
are presented, both showing a good agreement for rime and glaze ice condition.
Overall, this model shows great potential to model ice accretion reasonably
under different icing conditions. Besides, the present method doesn't require
analytic metric terms, and can be easily coupled to existing finite volume
solvers for logically Cartesian meshes
A sufficient condition for free-stream preserving in the nonlinear conservative finite difference schemes on curvilinear grids
In simulations of compressible flows, the conservative finite difference
method (FDM) based on the nonlinear upwind schemes, e.g. WENO5, might violate
free-stream preserving (FP), due to the loss of the geometric conservation law
(GCL) identity when applied on the curvilinear grids. Although some techniques
on FP have been proposed previously, no general rule is given for this issue.
In this paper, by rearranging the upwind dissipation of the nonlinear schemes
as a combination of sub-stencil reconstructions (taking WENO5 as an example),
it can be proved that the upwind dissipation diminishes under the uniform flow
condition if the metrics yield an identical value under the same schemes with
these reconstructions, making the free-stream condition be preserved. According
to this sufficient condition, the novel FP metrics are constructed for WENO5
and WENO7. By this means the original forms of these WENO schemes can be kept.
In addition, the accuracy of these schemes can be retained as well with a
simple accuracy compensation by replacing the central part fluxes with a
high-order one. Various validations indicate that the present FP schemes retain
the great capability to resolve the smooth regions accurately and capture the
discontinuities robustly
A species-clustered ODE solver for large-scale chemical kinetics using detailed mechanisms
In this study, a species-clustered ordinary differential equations (ODE)
solver for chemical kinetics with large detailed mechanisms based on
operator-splitting is presented. The ODE system is split into clusters of
species by using graph partition methods which has been intensively studied in
areas of model reduction, parameterization and coarse-graining, etc. , such as
diffusion maps based on the concept of Markov random walk. Definition of the
weight (similarity) matrix is application-driven and according to chemical
kinetics. Each cluster of species is then integrated by VODE, an implicit
solver which is intractable and costly for large systems of many species and
reactions. Expected speedup in computational efficiency is observed by
numerical experiments on three zero-dimensional (0D) auto-ignition problems,
considering the detailed hydrocarbon/air combustion mechanisms in varying
scales, from 53 species with 325 reactions of methane to 2115 species with 8157
reactions of n-hexadecane.Comment: 28 pages and 14 figure
Reformulated dissipation for the free-stream preserving of the conservative finite difference schemes on curvilinear grids
In this paper, we develop a new free-stream preserving (FP) method for
high-order upwind conservative finite-difference (FD) schemes on the
curvilinear grids. This FP method is constrcuted by subtracting a reference
cell-face flow state from each cell-center value in the local stencil of the
original upwind conservative FD schemes, which effectively leads to a
reformulated dissipation. It is convenient to implement this method, as it does
not require to modify the original forms of the upwind schemes. In addition,
the proposed method removes the constraint in the traditional FP conservative
FD schemes that require a consistent discretization of the mesh metrics and the
fluxes. With this, the proposed method is more flexible in simulating the
engineering problems which usually require a low-order scheme for their
low-quality mesh, while the high-order schemes can be applied to approximate
the flow states to improve the resolution. After demonstrating the strict FP
property and the order of accuracy by two simple test cases, we consider
various validation cases, including the supersonic flow around the cylinder,
the subsonic flow past the three-element airfoil, and the transonic flow around
the ONERA M6 wing, etc., to show that the method is suitable for a wide range
of fluid dynamic problems containing complex geometries. Moreover, these test
cases also indicate that the discretization order of the metrics have no
significant influences on the numerical results if the mesh resolution is not
sufficiently large
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