1,258 research outputs found
A quasi-conservative discontinuous Galerkin method for multi-component flows using the non-oscillatory kinetic flux
In this paper, a high order quasi-conservative discontinuous Galerkin (DG)
method using the non-oscillatory kinetic flux is proposed for the 5-equation
model of compressible multi-component flows with Mie-Gr\"uneisen equation of
state. The method mainly consists of three steps: firstly, the DG method with
the non-oscillatory kinetic flux is used to solve the conservative equations of
the model; secondly, inspired by Abgrall's idea, we derive a DG scheme for the
volume fraction equation which can avoid the unphysical oscillations near the
material interfaces; finally, a multi-resolution WENO limiter and a
maximum-principle-satisfying limiter are employed to ensure oscillation-free
near the discontinuities, and preserve the physical bounds for the volume
fraction, respectively. Numerical tests show that the method can achieve high
order for smooth solutions and keep non-oscillatory at discontinuities.
Moreover, the velocity and pressure are oscillation-free at the interface and
the volume fraction can stay in the interval [0,1].Comment: 41 pages, 70 figure
Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular Meshes
In this article we present a new class of high order accurate
Arbitrary-Eulerian-Lagrangian (ALE) one-step WENO finite volume schemes for
solving nonlinear hyperbolic systems of conservation laws on moving two
dimensional unstructured triangular meshes. A WENO reconstruction algorithm is
used to achieve high order accuracy in space and a high order one-step time
discretization is achieved by using the local space-time Galerkin predictor.
For that purpose, a new element--local weak formulation of the governing PDE is
adopted on moving space--time elements. The space-time basis and test functions
are obtained considering Lagrange interpolation polynomials passing through a
predefined set of nodes. Moreover, a polynomial mapping defined by the same
local space-time basis functions as the weak solution of the PDE is used to map
the moving physical space-time element onto a space-time reference element. To
maintain algorithmic simplicity, the final ALE one-step finite volume scheme
uses moving triangular meshes with straight edges. This is possible in the ALE
framework, which allows a local mesh velocity that is different from the local
fluid velocity. We present numerical convergence rates for the schemes
presented in this paper up to sixth order of accuracy in space and time and
show some classical numerical test problems for the two-dimensional Euler
equations of compressible gas dynamics.Comment: Accepted by "Communications in Computational Physics
Numerical Simulations of Shock and Rarefaction Waves Interacting With Interfaces in Compressible Multiphase Flows
Developing a highly accurate numerical framework to study multiphase mixing in high speed flows containing shear layers, shocks, and strong accelerations is critical to many scientific and engineering endeavors. These flows occur across a wide range of scales: from tiny bubbles in human tissue to massive stars collapsing. The lack of understanding of these flows has impeded the success of many engineering applications, our comprehension of astrophysical and planetary formation processes, and the development of biomedical technologies. Controlling mixing between different fluids is central to achieving fusion energy, where mixing is undesirable, and supersonic combustion, where enhanced mixing is important. Iron, found throughout the universe and a necessary component for life, is dispersed through the mixing processes of a dying star. Non-invasive treatments using ultrasound to induce bubble collapse in tissue are being developed to destroy tumors or deliver genes to specific cells. Laboratory experiments of these flows are challenging because the initial conditions and material properties are difficult to control, modern diagnostics are unable to resolve the flow dynamics and conditions, and experiments of these flows are expensive. Numerical simulations can circumvent these difficulties and, therefore, have become a necessary component of any scientific challenge. Advances in the three fields of numerical methods, high performance computing, and multiphase flow modeling are presented: (i) novel numerical methods to capture accurately the multiphase nature of the problem; (ii) modern high performance computing paradigms to resolve the disparate time and length scales of the physical processes; (iii) new insights and models of the dynamics of multiphase flows, including mixing through hydrodynamic instabilities. These studies have direct applications to engineering and biomedical fields such as fuel injection problems, plasma deposition, cancer treatments, and turbomachinery.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133458/1/marchdf_1.pd
Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity
The aim of this paper is to compare a hyperelastic with a hypoelastic model
describing the Eulerian dynamics of solids in the context of non-linear
elastoplastic deformations. Specifically, we consider the well-known
hypoelastic Wilkins model, which is compared against a hyperelastic model based
on the work of Godunov and Romenski. First, we discuss some general conceptual
differences between the two approaches. Second, a detailed study of both models
is proposed, where differences are made evident at the aid of deriving a
hypoelastic-type model corresponding to the hyperelastic model and a particular
equation of state used in this paper. Third, using the same high order ADER
Finite Volume and Discontinuous Galerkin methods on fixed and moving
unstructured meshes for both models, a wide range of numerical benchmark test
problems has been solved. The numerical solutions obtained for the two
different models are directly compared with each other. For small elastic
deformations, the two models produce very similar solutions that are close to
each other. However, if large elastic or elastoplastic deformations occur, the
solutions present larger differences.Comment: 14 figure
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