An adaptive mesh refinement benchmark for modern parallel programming languages

A parallel implicit adaptive mesh refinement (AMR) algorithm is described for the system of partial-differential equations governing steady two-dimensional compressible gaseous flows. The AMR algorithm uses an upwind finite-volume spatial discretization procedure in conjunction with limited linear solution reconstruction and Riemann-solver based flux functions to solve the governing equations on multi-block mesh composed of structured curvilinear blocks with quadrilateral computational cells. A flexible block-based hierarchical data structure is used to facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. A Jacobian-free inexact Newton method is used to solve the system of nonlinear equations arising from this finite-volume spatial discretization procedure and a preconditioned generalized minimal residual (GMRES) method is used to solve the resulting non-symmetric system of linear equations at each step of the Newton algorithm. An additive Schwarz global preconditioner with variable overlap is used in conjunction with block-fill incomplete lower-upper (BFILU) type preconditioners based on the Jacobian of the first-order upwind scheme for each sub-domain. The Schwarz preconditioning and block-based data structure readily allow efficient and scalable parallel implementations of the implicit AMR approach on distributed-memory multi-processor architectures. Numerical results will be described for several flow cases, demonstrating both the effectiveness of the mesh adaptation and algorithm parallel performance. The proposed parallel implicit AMR method allows for anisotropic mesh refinement and is well suited for predicting complex flows with disparate spatial and temporal scales.

We describe the development and implementation of a block-based adaptive mesh refinement (AMR) algorithm for solving the discrete ordinates neutral particle transport equation. AMR algorithms allow mesh refinement in areas of interest without requiring the extension of this refinement throughout the entire problem geometry, minimizing the number of computational cells required for calculations. The block-based AMR algorithm described here is a hybrid between traditional cell or patch-based approaches and is designed to allow an efficient parallel solution of the transport equation while still reducing the cell count.This paper discusses the data structure implementation and CPU/memory efficiency for our Block AMR method, the equations and procedures used in mapping edge fluxes between blocks of different refinement levels for both diamond and linear discontinuous spatial discretizations, effects of AMR on mesh convergence, and our approach to parallelization. Comparisons between our Block AMR method and a traditional single-level mesh are presented for a sample brachytherapy problem. The Block AMR results are shown to be significantly faster for this problem (on at least a few processors), while still returning an accurate solution.

In prior-research the authors have demonstrated that, for stencil-based numerical solvers for Partial Differential Equations (PDEs), the parallel performance can be significantly improved by selecting sub-domains that are not cubic in shape (Saxena et. al., HPCS 2016, pp. 875-885). This is achieved through accounting for cache utilization in both the message passing and the computational kernel, where it is demonstrated that the optimal domain decompositions not only depend on the communication and load balance but also on the cache-misses, amongst other factors. In this work we demonstrate that those conclusions may also be extended to more advanced numerical discretizations, based upon Adaptive Mesh Refinement (AMR). In particular, we show that when basing our AMR strategy on the local refinement of patches of the mesh, the optimal patch shape is not typically cubic. We provide specific examples, with accompanying explanation, to show that communication minimizing strategies are not necessarily the best choice when applying AMR in parallel. All numerical tests undertaken in this work are based upon the open source BoxLib library.

Towards adaptive kinetic-fluid simulations of weakly ionized plasmas

One of the main aspects in the development of modern diesel engines has been the direct injection systems, due to its influence in the atomization and evaporation processes. The study of all physical and chemical phenomena involved in the scarce milliseconds that the diesel injection last allows a better understanding of the injection. Therefore, it allows a better control of the combustion process (i.e. a higher energy efficiency and lower pollutant emissions).\n\nDespite its relevance, there are however many uncertainties regarding the internal flow and the air-fuel mixing process, caused by the small size of the injector ducts, the high injection pressures (i.e. high velocities in the ducts) and the transient nature of the diesel injection influenced by the needle lift. Hence, the use of numerical simulations provides invaluable data to improve the knowledge of the process. Therefore, CFD (computational fluid dynamics) simulations are each day commoner.\n\nIn order to achieve the purpose of the present thesis, a comparative study of the injection process of three different diesel nozzles through a new CFD code, which simplifies the mesh creation and endows the simulation with the possibility of a dynamic mesh through the use of an AMR (adaptive mesh refinement) algorithm that refines the mesh where high gradients of the physical fields (velocity, concentration, etc.) exist, has been performed. This study has allowed to study the internal flow and diesel spray (in evaporative and non-evaporative conditions) and enlightened the relation between the nozzle geometry and the calibration parameters of the different sub-models used in the simulations (atomization, coalescence, evaporation, etc.).\n\nThe computational study shows a good agreement between the experimental data and the computational results, in particular for the transient internal flow study, where the AMR algorithm has allowed a run-time mesh generation and thus the study of the needle lift without a negative influence in the mesh quality. Furthermore, the computational study of the diesel spray through an eulerian-lagrangian approach with three different nozzle geometries arose the existing relation between the spray sub-models and the nozzle geometry, so that the spray calibration was generalized for every injection system (injector).

The goal of this study is to develop advanced numerical models and algorithms to improve the accuracy of engine spray combustion simulation. This study developed a large eddy simulation (LES) turbulence model and adaptive mesh refinement (AMR) algorithms to enhance the accuracy and computational efficiency of engine simulation. The LES approach for turbulence modeling is advantageous over the traditional Reynolds Averaged Navier Stokes (RANS) approach due to its capability to obtain more detailed flow information by resolving large-scale structures which are strongly geometry dependent. The current LES approach used a one-equation, non-viscosity, dynamic structure model for the sub-grid stress tensor and also used a gradient method for the sub-grid scalar fluxes. The LES implementation was validated by comparing the predicted spray penetrations and structures in a non-evaporating diesel spray. The present LES model, when coupled with spray breakup and detailed chemistry models, were able to predict the overall cylinder pressure history, heat release rate data, and the trends of NOx and soot emissions with respect to different injection timings and EGR levels in a heavy-duty diesel engine. Results also indicated that the LES model could predict the unsteadiness of in-cylinder flows and have the potential to provide more detailed flow structures compared to the RANS model. AMR algorithms were also developed to improve transient engine spray simulation. It is known that inadequate spatial resolution can cause inaccuracy in spray simulation using the stochastic Lagrangian particle approach due to the over-estimated diffusion and inappropriate

Quantitative 3D phase field modelling of solidification using next-generation adaptive mesh refinement

Flash memory-based computing-in-memory (CIM) architectures have gained popularity due to their remarkable performance in various computation tasks of data processing, including machine learning, neuron networks, and scientific calculations. Especially in the partial differential equation (PDE) solver that has been widely utilized in scientific calculations, high accuracy, processing speed, and low power consumption are the key requirements. This work proposes a novel flash memory-based PDE solver to implement PDE with high accuracy, low power consumption, and fast iterative convergence. Moreover, considering the increasing current noise in nanoscale devices, we investigate the robustness against the noise in the proposed PDE solver. The results show that the noise tolerance limit of the solver can reach more than five times that of the conventional Jacobi CIM solver. Overall, the proposed flash memory-based PDE solver offers a promising solution for scientific calculations that require high accuracy, low power consumption, and good noise immunity, which could help to develop flash-based general computing.

A new adaptive local mesh refinement algorithm and its application on fourth order thin film flow problem

The intensity variation in a scanning electron microscope is a complex function of sample topography and composition. Measurement accuracy is improved when an explicit accounting for the relationship between signal and measurand is made. Because the determinants of the signal are many, the theoretical understanding usually takes the form of a simulator. For samples with nonconducting regions that charge, one phase of the simulation is finite element analysis to compute the electric field. The size of the finite element mesh, and consequently computation time, can be reduced through the use of adaptive mesh refinement. We present a new a posteriori local error estimator and adaptive mesh refinement algorithm for the scanning electron microscope simulation. This error estimate is designed to minimize the error in the electron trajectories, rather than the energy norm of the error that traditional error estimators minimize. Using a test problem with a known exact solution, we show that the adaptive mesh can achieve the same error in electron trajectories as a carefully designed hand-graded mesh while using 3.5 times fewer vertices and 2.25 times less computation time.

Summary An adaptive three-dimensional mesh refinement method based on the law of mass conservation has been introduced and tested using some analytical velocity fields as accurate in identifying singular point, asymptotic plane and drawing closed streamlines. This paper further investigates the adaptive mesh refinement method using a velocity field that is due to a uniform strain and a point vortex. Similar results have been obtained.

ABSTRACTThis paper presents an adaptive mesh refinement (AMR) algorithm to solve the non-isothermal multiphase flows in heterogeneous porous media comprising different rock types. To address the discontinuity coming from different rock types, we found that the ratios of relative permeability and oil-gas capillary pressure are continuous; hence they are chosen as the judging values for the regridding purpose. Moreover, because of the tensorial permeability and the complex topology of the AMR grid, a coupling flux solution based on the multipoint flux approximation was carefully designed. Numerical examples revealed the accuracy and efficiency of the proposed AMR algorithm.

This paper describes an adaptive algorithm for optimal control of time‐dependent partial differential‐algebraic equation (PDAE) systems. A direct method based on a modified multiple shooting type technique and sequential quadratic programming (SQP) is used for solving the optimal control problem, while an adaptive mesh refinement (AMR) algorithm is employed to dynamically adapt the spatial integration mesh. Issues of coupling the AMR solver to the optimization algorithm are addressed. For time‐dependent PDAEs which can benefit from the use of an adaptive mesh, the resulting method is shown to be highly efficient. Copyright © 2003 John Wiley & Sons, Ltd.

Enhanced anisotropic block-based adaptive mesh refinement for three-dimensional inviscid and viscous compressible flows

This document presents a description of the octree mesh-generation capabilities and of the parallel mesh adaptation kernel. As it is discussed in Section 1.3.2 of part B of the project proposal there are two parallel research lines aimed at developing scalable adaptive mesh refinement (AMR) algorithms and implementations. The first one is based on using octree-based mesh generation and adaptation for the whole simulation in combination with unfitted finite element methods (FEMs) and the use of algebraic constraints to deal with non-conformity of spaces. On the other hand the second strategy is based on the use of an initial octree mesh that, after make it conforming through the addition of templatebased tetrahedral refinements, is adapted anisotropically during the calculation. Regarding the first strategy the following items are included: