335 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
Implementation of a low-mach number modification for high-order finite-volume schemes for arbitrary hybrid unstructured meshes
An implementation of a novel low-mach number treatment for high-order finite-volume schemes using arbitrary hybrid unstructured meshes is presented in this paper. Low-Mach order modifications for Godunov type finite-volume schemes have been implemented successfully for structured and unstructured meshes, however the methods break down for hybrid mesh topologies containing multiple element types. The modification is applied to the UCNS3D finite-volume framework for compressible flow configurations, which have been shown as very capable of handling any type of grid topology. The numerical methods under consideration are the Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and the Weighted Essentially Non-Oscillatory (WENO) schemes for two-dimensional mixed-element type unstructured meshes. In the present study the HLLC Approximate Riemann Solver is used with an explicit TVD Runge-Kutta 3rd-order method due to its excellent scalability. These schemes (up to 5th-order) are applied to well established two-dimensional and three-dimensional test cases. The challenges that occur when applying these methods to low-mach flow configurations is thoroughly analysed and possible improvements and further test cases are suggested
Addressing the challenges of implementation of high-order finite volume schemes for atmospheric dynamics of unstructured meshes
The solution of the non-hydrostatic compressible Euler equations using Weighted Essentially Non-Oscillatory (WENO) schemes in two and three-dimensional unstructured meshes, is presented. Their key characteristics are their simplicity; accuracy; robustness; non-oscillatory properties; versatility in handling any type of grid topology; computational and parallel efficiency. Their defining characteristic is a non-linear combination of a series of high-order reconstruction polynomials arising from a series of reconstruction stencils. In the present study an explicit TVD Runge-Kutta 3rd -order method is employed due to its lower computational resources requirement compared to implicit type time advancement methods. The WENO schemes (up to 5th -order) are applied to the two dimensional and three dimensional test cases: a 2D rising
ADER-WENO Finite Volume Schemes with Space-Time Adaptive Mesh Refinement
We present the first high order one-step ADER-WENO finite volume scheme with
Adaptive Mesh Refinement (AMR) in multiple space dimensions. High order spatial
accuracy is obtained through a WENO reconstruction, while a high order one-step
time discretization is achieved using a local space-time discontinuous Galerkin
predictor method. Due to the one-step nature of the underlying scheme, the
resulting algorithm is particularly well suited for an AMR strategy on
space-time adaptive meshes, i.e.with time-accurate local time stepping. The AMR
property has been implemented 'cell-by-cell', with a standard tree-type
algorithm, while the scheme has been parallelized via the Message Passing
Interface (MPI) paradigm. The new scheme has been tested over a wide range of
examples for nonlinear systems of hyperbolic conservation laws, including the
classical Euler equations of compressible gas dynamics and the equations of
magnetohydrodynamics (MHD). High order in space and time have been confirmed
via a numerical convergence study and a detailed analysis of the computational
speed-up with respect to highly refined uniform meshes is also presented. We
also show test problems where the presented high order AMR scheme behaves
clearly better than traditional second order AMR methods. The proposed scheme
that combines for the first time high order ADER methods with space--time
adaptive grids in two and three space dimensions is likely to become a useful
tool in several fields of computational physics, applied mathematics and
mechanics.Comment: With updated bibliography informatio
A Continuous/Discontinuous FE Method for the 3D Incompressible Flow Equations
A projection scheme for the numerical solution of the incompressible Navier-Strokes equation is presented. Finite element discontinuous Galerkin (dG) discretization for the velocity in the momentum equations is employed. The incompressibility constraint is enforced by numerically solving the Poisson equation for pressure using a continuous Galerkin (cG) discretization. The main advantage of the method is that is does not require the velocity and pressure approximation spaces to satisfy the usual inf-sup condition, thus equal order finite element approximations for both velocity and pressure can be used. Furthermore, by using cG discretization for the Poisson equation, no auxiliary equations are needed as it is required for dG approximations of second order derivatives. In order to enable large time steps for time marching to steady-state and time evolving problems, implicit scheme is used in connection with high order implicit RK methods. Numerical tests demonstrate that the overall scheme is accurate and computationally efficient
High-order incompressible computational fluid dynamics on modern hardware architectures
In this thesis, a high-order incompressible Navier-Stokes solver is developed in the
Python-based PyFR framework. The solver is based on the artificial compressibility
formulation with a Flux Reconstruction (FR) discretisation in space and explicit
dual time stepping in time. In order to reduce time to solution, explicit convergence
acceleration techniques are developed and implemented. These techniques include
polynomial multigrid, a novel locally adaptive pseudo-time stepping approach and
novel stability-optimised Runge-Kutta schemes.
Choices regarding the numerical methods and implementation are motivated as
follows. Firstly, high-order FR is selected as the spatial discretisation due to its low
dissipation and ability to work with unstructured meshes of complex geometries. Be-
ing discontinuous, it also allows the majority of computation to be performed locally.
Secondly, convergence acceleration techniques are restricted to explicit methods in
order to retain the spatial locality provided by FR, which allows efficient harnessing
of the massively parallel compute capability of modern hardware. Thirdly, the solver
is implemented in the PyFR framework with cross-platform support such that it can
run on modern heterogeneous systems via an MPI + X model, with X being CUDA,
OpenCL or OpenMP. As such, it is well-placed to remain relevant in an era of rapidly
evolving hardware architectures.
The new software constitutes the first high-order accurate cross-platform imple-
mentation of an incompressible Navier-Stokes solver via artificial compressibility. The
solver and the convergence acceleration techniques are validated for a range of turbu-
lent test cases. Furthermore, performance of the convergence acceleration techniques
is assessed with a 2D cylinder test case, showing speed-up factors of over 20 relative
to global RK4 pseudo-time stepping when all of the technologies are combined. Fi-
nally, a simulation of the DARPA SUBOFF submarine model is undertaken using the
solver and all convergence acceleration techniques. Excellent agreement with previ-
ous studies is obtained, demonstrating that the technology can be used to conduct
high-fidelity implicit Large Eddy Simulation of industrially relevant problems at scale
using hundreds of GPUs.Open Acces
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
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