2,918 research outputs found
High-Order Unstructured Lagrangian One-Step WENO Finite Volume Schemes for Non-Conservative Hyperbolic Systems: Applications to Compressible Multi-Phase Flows
In this article we present the first better than second order accurate
unstructured Lagrangian-type one-step WENO finite volume scheme for the
solution of hyperbolic partial differential equations with non-conservative
products. The method achieves high order of accuracy in space together with
essentially non-oscillatory behavior using a nonlinear WENO reconstruction
operator on unstructured triangular meshes. High order accuracy in time is
obtained via a local Lagrangian space-time Galerkin predictor method that
evolves the spatial reconstruction polynomials in time within each element. The
final one-step finite volume scheme is derived by integration over a moving
space-time control volume, where the non-conservative products are treated by a
path-conservative approach that defines the jump terms on the element
boundaries. The entire method is formulated as an Arbitrary-Lagrangian-Eulerian
(ALE) method, where the mesh velocity can be chosen independently of the fluid
velocity.
The new scheme is applied to the full seven-equation Baer-Nunziato model of
compressible multi-phase flows in two space dimensions. The use of a Lagrangian
approach allows an excellent resolution of the solid contact and the resolution
of jumps in the volume fraction. The high order of accuracy of the scheme in
space and time is confirmed via a numerical convergence study. Finally, the
proposed method is also applied to a reduced version of the compressible
Baer-Nunziato model for the simulation of free surface water waves in moving
domains. In particular, the phenomenon of sloshing is studied in a moving water
tank and comparisons with experimental data are provided
Study of full implicit petroleum engineering finite volume scheme for compressible two phase flow in porous media
An industrial scheme, to simulate the two compressible phase flow in porous
media, consists in a finite volume method together with a phase-by-phase
upstream scheme. The implicit finite volume scheme satisfies industrial
constraints of robustness. We show that the proposed scheme satisfy the maximum
principle for the saturation, a discrete energy estimate on the pressures and a
function of the saturation that denote capillary terms. These stabilities
results allow us to derive the convergence of a subsequence to a weak solution
of the continuous equations as the size of the discretization tends to zero.
The proof is given for the complete system when the density of the each phase
depends on the own pressure
Numerical simulation of liquid sloshing in a partially filled container with inclusion of compressibility effects
A numerical scheme of study is developed to model compressible two-fluid flows simulating liquid sloshing in a partially filled tank. For a two-fluid system separated by an interface as in the case of sloshing, not only a Mach-uniform scheme is required, but also an effective way to eliminate unphysical numerical oscillations near the interface. By introducing a preconditioner, the governing equations expressed in terms of primitive variables are solved for both fluids (i.e. water, air, gas etc.) in a unified manner. In order to keep the interface sharp and to eliminate unphysical numerical oscillations in unsteady fluid flows, the non-conservative implicit Split Coefficient Matrix Method (SCMM) is modified to construct a flux difference splitting scheme in the dual time formulation. The proposed numerical model is evaluated by comparisons between numerical results and measured data for sloshing in an 80% filled rectangular tank excited at resonance frequency. Through similar comparisons, the investigation is further extended by examining sloshing flows excited by forced sway motions in two different rectangular tanks with 20% and 83% filling ratios. These examples demonstrate that the proposed method is suitable to capture induced free surface waves and to evaluate sloshing pressure loads acting on the tank walls and ceiling
Institute for Computational Mechanics in Propulsion (ICOMP)
The Institute for Computational Mechanics in Propulsion (ICOMP) is a combined activity of Case Western Reserve University, Ohio Aerospace Institute (OAI) and NASA Lewis. The purpose of ICOMP is to develop techniques to improve problem solving capabilities in all aspects of computational mechanics related to propulsion. The activities at ICOMP during 1991 are described
Analysis of the incompressibility constraint in the Smoothed Particle Hydrodynamics method
Smoothed particle hydrodynamics is a particle-based, fully Lagrangian, method
for fluid-flow simulations. In this work, fundamental concepts of the method
are first briefly recalled. Then, we present a thorough comparison of three
different incompressibility treatments in SPH: the weakly compressible
approach, where a suitably-chosen equation of state is used; and two truly
incompressible methods, where the velocity field projection onto a
divergence-free space is performed. A noteworthy aspect of the study is that,
in each incompressibility treatment, the same boundary conditions are used (and
further developed) which allows a direct comparison to be made. Problems
associated with implementation are also discussed and an optimal choice of the
computational parameters has been proposed and verified. Numerical results show
that the present state-of-the-art truly incompressible method (based on a
velocity correction) suffer from density accumulation errors. To address this
issue, an algorithm, based on a correction for both particle velocities and
positions, is presented. The usefulness of this density correction is examined
and demonstrated in the last part of the paper
Hypervelocity Richtmyer–Meshkov instability
The Richtmyer-Meshkov instability is numerically investigated for strong shocks, i.e., for hypervelocity cases. To model the interaction of the flow with non-equilibrium chemical effects typical of high-enthalpy flows, the Lighthill-Freeman ideal dissociating gas model is employed. Richtmyer's linear theory and the impulse model are extended to include equilibrium dissociation chemistry. Numerical simulations of the compressible Euler equations indicate no period of linear growth even for amplitude to wavelength ratios as small as one percent. For large Atwood numbers, dissociation causes significant changes in density and temperature, but the change in growth of the perturbations is small. A Mach number scaling for strong shocks is presented which holds for frozen chemistry at high Mach numbers. A local analysis is used to determine the initial baroclinic circulation generation for interfaces corresponding to both positive and negative Atwood ratios
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