Parallel algorithm for numerical simulation of 3D incompressible flows

2004 ◽  
pp. 65-72 ◽  
Author(s):  
T.G. Elizarova ◽  
O.Yu. Milyukova
Keyword(s):  
Numerical Simulation ◽  
Parallel Algorithm ◽  
Incompressible Flows

scholarly journals Flow topologies in primary atomization of liquid jets: a direct numerical simulation analysis

2018 ◽  
Vol 859 ◽  
pp. 819-838 ◽  
Author(s):  
Josef Hasslberger ◽  
Sebastian Ketterl ◽  
Markus Klein ◽  
Nilanjan Chakraborty
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Incompressible Flows ◽  
Flow Structures ◽  
Liquid Jets ◽  
Small Scale ◽  
Flow Topology ◽  
Local Flow ◽  
Turbulent Length Scale

The local flow topology analysis of the primary atomization of liquid jets has been conducted using the invariants of the velocity-gradient tensor. All possible small-scale flow structures are categorized into two focal and two nodal topologies for incompressible flows in both liquid and gaseous phases. The underlying direct numerical simulation database was generated by the one-fluid formulation of the two-phase flow governing equations including a high-fidelity volume-of-fluid method for accurate interface propagation. The ratio of liquid-to-gas fluid properties corresponds to a diesel jet exhausting into air. Variation of the inflow-based Reynolds number as well as Weber number showed that both these non-dimensional numbers play a pivotal role in determining the nature of the jet break-up, but the flow topology behaviour appears to be dominated by the Reynolds number. Furthermore, the flow dynamics in the gaseous phase is generally less homogeneous than in the liquid phase because some flow regions resemble a laminar-to-turbulent transition state rather than fully developed turbulence. Two theoretical models are proposed to estimate the topology volume fractions and to describe the size distribution of the flow structures, respectively. In the latter case, a simple power law seems to be a reasonable approximation of the measured topology spectrum. According to that observation, only the integral turbulent length scale would be required as an input for the a priori prediction of the topology size spectrum.

Numerical simulation of incompressible flows within simple boundaries: accuracy

1971 ◽  
Vol 49 (1) ◽  
pp. 75-112 ◽  
Author(s):  
Steven A. Orszag
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Spectral Methods ◽  
Degrees Of Freedom ◽  
Incompressible Flows ◽  
Finite Difference Methods ◽  
Fourier Method ◽  
Passive Scalar ◽  
Mathematical Basis ◽  
Improved Accuracy

Galerkin (spectral) methods for numerical simulation of incompressible flows within simple boundaries are shown to possess many advantages over existing finite-difference methods. In this paper, the accuracy of Galerkin approximations obtained from truncated Fourier expansions is explored. Accuracy of simulation is tested empirically using a simple scalar-convection test problem and the Taylor–Green vortex-decay problem. It is demonstrated empirically that the Galerkin (Fourier) equations involving Np degrees of freedom, where p is the number of space dimensions, give simulations at least as accurate as finite-difference simulations involving (2N)p degrees of freedom. The theoretical basis for the improved accuracy of the Galerkin (Fourier) method is explained. In particular, the nature of aliasing errors is examined in detail. It is shown that ‘aliasing’ errors need not be errors at all, but that aliasing should be avoided in flow simulations. An eigenvalue analysis of schemes for simulation of passive scalar convection supplies the mathematical basis for the improved accuracy of the Galerkin (Fourier) method. A comparison is made of the computational efficiency of Galerkin and finite-difference simulations, and a survey is given of those problems where Galerkin methods are likely to be applied most usefully. We conclude that numerical simulation of many of the flows of current interest is done most efficiently and accurately using the spectral methods advocated here.

scholarly journals GPU Parallelization Nested Decomposition Method for Solving Large Linear Systems in Reservoir Numerical Simulation

2019 ◽  
Vol 23 (3) ◽  
pp. 249-257
Author(s):  
Xin Shi ◽  
Yuan Di
Keyword(s):  
Numerical Simulation ◽  
Parallel Algorithm ◽  
Linear Equations ◽  
Parallel Architecture ◽  
Residual Pressure ◽  
Linear Solution ◽  
Structured Grid ◽  
Grid Model ◽  
Preprocessing Method ◽  
Large Linear Systems

This paper designs a highly parallel Nested Factorization (NF) to solve large linear equations generated in reservoir numerical simulation problems. The NF method is a traditional linear solution preprocessing method for reservoir numerical simulation problems, and has regained attention in recent years due to its potential to extend to parallel architectures such as GPUs (Graphics Processor Units). The parallel algorithm of this paper is based on the MPNF (Massively Parallel Nested Factorization) framework proposed by Appleya (Appleyard, Appleyard, Wakefield, & Desitter, 2011). The MPNF algorithm designed in this paper focuses on its efficient implementation on the GPU parallel architecture. Its features include: using a custom matrix structure to achieve merge access, improving access bottlenecks and improving the efficiency of the SpMV algorithm. It is also applicable to the two-stage preprocessing method CPR. (Constrain Pressure Residual) pressure solution and global preprocessing stage; the MPNF method is extended to the solution of 2.5-dimensional unstructured grid problem. The parallel algorithm in this paper has been integrated into the reservoir numerical simulator. For the SPE10 (million grid, highly heterogeneous) standard example, the GPU-based parallel NF algorithm is in the structured grid model and the equivalent 2.5-dimensional non- On the structured grid model, compared with the serial version of the NF method, the acceleration ratios of 19.8 and 17.0 times were obtained respectively; compared with the mainstream serial solution method, the efficiency was also improved by 2 to 3 times.

PARALLEL SIMULATION OF EXPLOSION IN AN UNLIMITED ATMOSPHERE

2010 ◽  
Vol 24 (13) ◽  
pp. 1349-1352 ◽  
Author(s):  
TIANBAO MA ◽  
CHENG WANG ◽  
GUANGLEI FEI ◽  
JIANGUO NING
Keyword(s):  
Numerical Simulation ◽  
Parallel Algorithm ◽  
Large Scale ◽  
Three Dimensional ◽  
Parallel Simulation ◽  
Data Dependency ◽  
Empirical Results ◽  
Parallel Speedup ◽  
Good Agreement ◽  
Impact Problem

In this paper, a parallel Eulerian hydrocode for the simulation of large scale complicated explosion and impact problem is developed. The data dependency in the parallel algorithm is studied in particular. As a test, the three dimensional numerical simulation of the explosion field in an unlimited atmosphere is performed. The numerical results are in good agreement with the empirical results, indicating that the proposed parallel algorithm in this paper is valid. Finally, the parallel speedup and parallel efficiency under different dividing domain areas are analyzed.

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