45 research outputs found
Hybrid Spectral Difference/Embedded Finite Volume Method for Conservation Laws
A novel hybrid spectral difference/embedded finite volume method is
introduced in order to apply a discontinuous high-order method for large scale
engineering applications involving discontinuities in the flows with complex
geometries. In the proposed hybrid approach, the finite volume (FV) element,
consisting of structured FV subcells, is embedded in the base hexahedral
element containing discontinuity, and an FV based high-order shock-capturing
scheme is employed to overcome the Gibbs phenomena. Thus, a discontinuity is
captured at the resolution of FV subcells within an embedded FV element. In the
smooth flow region, the SD element is used in the base hexahedral element.
Then, the governing equations are solved by the SD method. The SD method is
chosen for its low numerical dissipation and computational efficiency
preserving high-order accurate solutions. The coupling between the SD element
and the FV element is achieved by the globally conserved mortar method. In this
paper, the 5th-order WENO scheme with the characteristic decomposition is
employed as the shock-capturing scheme in the embedded FV element, and the
5th-order SD method is used in the smooth flow field.
The order of accuracy study and various 1D and 2D test cases are carried out,
which involve the discontinuities and vortex flows. Overall, it is shown that
the proposed hybrid method results in comparable or better simulation results
compared with the standalone WENO scheme when the same number of solution DOF
is considered in both SD and FV elements.Comment: 27 pages, 17 figures, 2 tables, Accepted for publication in the
Journal of Computational Physics, April 201
Development of a Chemically Reacting Flow Solver on the Graphic Processing Units
The focus of the current research is to develop a numerical framework on the Graphic Processing Units (GPU) capable of modeling chemically reacting flow. The framework incorporates a high-order finite volume method coupled with an implicit solver for the chemical kinetics. Both the fluid solver and the kinetics solver are designed to take advantage of the GPU architecture to achieve high performance. The structure of the numerical framework is shown, detailing different aspects of the optimization implemented on the solver. The mathematical formulation of the core algorithms is presented along with a series of standard test cases, including both nonreactive and reactive flows, in order to validate the capability of the numerical solver. The performance results obtained with the current framework show the parallelization efficiency of the solver and emphasize the capability of the GPU in performing scientific calculations.
Distribution A: Approved for public release; distribution unlimited. PA #1117
Evaluation of finite difference based asynchronous partial differential equations solver for reacting flows
Next-generation exascale machines with extreme levels of parallelism will
provide massive computing resources for large scale numerical simulations of
complex physical systems at unprecedented parameter ranges. However, novel
numerical methods, scalable algorithms and re-design of current state-of-the
art numerical solvers are required for scaling to these machines with minimal
overheads. One such approach for partial differential equations based solvers
involves computation of spatial derivatives with possibly delayed or
asynchronous data using high-order asynchrony-tolerant (AT) schemes to
facilitate mitigation of communication and synchronization bottlenecks without
affecting the numerical accuracy. In the present study, an effective
methodology of implementing temporal discretization using a multi-stage
Runge-Kutta method with AT schemes is presented. Together these schemes are
used to perform asynchronous simulations of canonical reacting flow problems,
demonstrated in one-dimension including auto-ignition of a premixture, premixed
flame propagation and non-premixed autoignition. Simulation results show that
the AT schemes incur very small numerical errors in all key quantities of
interest including stiff intermediate species despite delayed data at
processing element (PE) boundaries. For simulations of supersonic flows, the
degraded numerical accuracy of well-known shock-resolving WENO (weighted
essentially non-oscillatory) schemes when used with relaxed synchronization is
also discussed. To overcome this loss of accuracy, high-order AT-WENO schemes
are derived and tested on linear and non-linear equations. Finally the novel
AT-WENO schemes are demonstrated in the propagation of a detonation wave with
delays at PE boundaries
High-order methods for diffuse-interface models in compressible multi-medium flows: a review
The diffuse interface models, part of the family of the front capturing methods, provide an efficient and robust framework for the simulation of multi-species flows. They allow the integration of additional physical phenomena of increasing complexity while ensuring discrete conservation of mass, momentum, and energy. The main drawback brought by the adoption of these models consists of the interface smearing, increasing with the simulation time, therefore, requiring a counteraction through the introduction of sharpening terms and a careful selection of the discretization level. In recent years, the diffuse interface models have been solved using several numerical frameworks including finite volume, discontinuous Galerkin, and hybrid lattice Boltzmann method, in conjunction with shock and contact wave capturing schemes. The present review aims to present the recent advancements of high-order accuracy schemes with the capability of solving discontinuities without the introduction of numerical instabilities and to put them in perspective for the solution of multi-species flows with the diffuse interface method.Engineering and Physical Sciences Research Council (EPSRC): 2497012.
Innovate UK: 263261.
Airbus U
An Application of Gaussian Process Modeling for High-order Accurate Adaptive Mesh Refinement Prolongation
We present a new polynomial-free prolongation scheme for Adaptive Mesh
Refinement (AMR) simulations of compressible and incompressible computational
fluid dynamics. The new method is constructed using a multi-dimensional
kernel-based Gaussian Process (GP) prolongation model. The formulation for this
scheme was inspired by the GP methods introduced by A. Reyes et al. (A New
Class of High-Order Methods for Fluid Dynamics Simulation using Gaussian
Process Modeling, Journal of Scientific Computing, 76 (2017), 443-480; A
variable high-order shock-capturing finite difference method with GP-WENO,
Journal of Computational Physics, 381 (2019), 189-217). In this paper, we
extend the previous GP interpolations and reconstructions to a new GP-based AMR
prolongation method that delivers a high-order accurate prolongation of data
from coarse to fine grids on AMR grid hierarchies. In compressible flow
simulations special care is necessary to handle shocks and discontinuities in a
stable manner. To meet this, we utilize the shock handling strategy using the
GP-based smoothness indicators developed in the previous GP work by A. Reyes et
al. We demonstrate the efficacy of the GP-AMR method in a series of testsuite
problems using the AMReX library, in which the GP-AMR method has been
implemented
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Gaussian Process Modeling for Upsampling Algorithms With Applications in Computer Vision and Computational Fluid Dynamics
Across a variety of fields, interpolation algorithms have been used to upsample lowresolution or coarse data fields. In this work, novel Gaussian Process based methodsare employed to solve a variety of upsampling problems. Specifically threeapplications are explored: coarse data prolongation in Adaptive Mesh Refinement(AMR) in the field of Computational Fluid Dynamics, accurate document imageupsampling to enhance Optical Character Recognition (OCR) accuracy, and fastand accurate Single Image Super Resolution (SISR). For AMR, a new, efficient,and “3rd order accurate” algorithm called GP-AMR is presented. Next, a novel,non-zero mean, windowed GP model is generated to upsample low resolution documentimages to generate a higher OCR accuracy, when compared to the industrystandard. Finally, a hybrid GP convolutional neural network algorithm is used togenerate a computationally efficient and high quality SISR model
Computational modeling of advanced, multi-material energetic materials and systems
The aim of this thesis is to develop and implement a robust reactive simulation tool that can aid in the design of explosive devices by numerically investigating the reactive mechanism of different explosive materials; study how detonation waves travel through them and determine how to initiate explosives with the smallest amount of booster material. These types of problems are numerically challenging to model and require multiple components that interact with each other. Multi-material models are necessary since shocks and detonation waves will travel through and impinge on material interfaces. High order and robust methods are needed to maintain sharp representations of these material boundaries. They need to be capable of numerically maintaining stable interfaces between high energy explosive materials and low density inerts such as air. This is a challenging problem since it involves strong wave interactions at the interface, large pressure and density gradients across the same, and non-linearity issues that result from the use of real equations of state. From a software developing point of view, consistent code infrastructure also needs to be followed to allow the ability to easily implement new models and modify existing ones. Also, given the multi-scaled nature of these types of problems, methods need to be efficient and scalable in both shared and distributed memory architectures for parallel computing.
The proposed parallel and robust numerical reactive hydrodynamic solver implementation maintains sharp solid and material interfaces. The solver is designed to run on distributed memory architectures using a simple yet efficient MPI communication implementation. Multiple level sets are used to track the evolution of material interfaces over time and represent internal solid regions. Approximate Riemann solvers and the Ghost Fluid Method or Overlap Domain Method are used to enforce appropriate interface boundary conditions. Ghost nodes are set by a new local and point-wise node sorting algorithm that decouples these nodes by establishing their connectivity to other ghost nodes. This approach allows us to enforce boundary conditions via a direct procedure removing the need to solve a coupled system of equations numerically. Issues concerning the use of reactive, non-ideal equations of state and their implementation in high explosive hydrodynamic codes are studied. The accuracy and fidelity of the solver is examined by simulating a series of explosive multi-material problems, showing good agreement between numerical results and experimental data
Continuous finite element subgrid basis functions for Discontinuous Galerkin schemes on unstructured polygonal Voronoi meshes
We propose a new high order accurate nodal discontinuous Galerkin (DG) method
for the solution of nonlinear hyperbolic systems of partial differential
equations (PDE) on unstructured polygonal Voronoi meshes. Rather than using
classical polynomials of degree N inside each element, in our new approach the
discrete solution is represented by piecewise continuous polynomials of degree
N within each Voronoi element, using a continuous finite element basis defined
on a subgrid inside each polygon. We call the resulting subgrid basis an
agglomerated finite element (AFE) basis for the DG method on general polygons,
since it is obtained by the agglomeration of the finite element basis functions
associated with the subgrid triangles. The basis functions on each sub-triangle
are defined, as usual, on a universal reference element, hence allowing to
compute universal mass, flux and stiffness matrices for the subgrid triangles
once and for all in a pre-processing stage for the reference element only.
Consequently, the construction of an efficient quadrature-free algorithm is
possible, despite the unstructured nature of the computational grid. High order
of accuracy in time is achieved thanks to the ADER approach, making use of an
element-local space-time Galerkin finite element predictor.
The novel schemes are carefully validated against a set of typical benchmark
problems for the compressible Euler and Navier-Stokes equations. The numerical
results have been checked with reference solutions available in literature and
also systematically compared, in terms of computational efficiency and
accuracy, with those obtained by the corresponding modal DG version of the
scheme