Comparative accuracy and performance assessment of the finite point method in compressible flow problems

Ortega, Enrique; Oñate, Eugenio; Idelsohn, Sergio; Flores, Roberto

doi:10.1016/j.compfluid.2013.10.024

Cited by 12 publications

(11 citation statements)

References 17 publications

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“…In this figure, it can also be noticed that the scalability of OpenMP on multi-core CPUs is not satisfactory since two eight-core CPUs only give a 4∼5× speedup compared to a single core on platform 2. This phenomenon is very similar to Ortega et al's observation that attainable speedups on multi-core CPUs will drop once the number of processor cores is over 4 due to the high cache miss rate and limited memory bandwidth of CPU (see figures 13 and 14 of [53]). …”

Section: Performance Analysissupporting

confidence: 76%

A GPU based compressible multiphase hydrocode for modelling violent hydrodynamic impact problems

Causon

Qian

et al. 2015

Computers & Fluids

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Highlights• A versatile compressible multiphase hydrocode for marine engineering impact problems.• Non-physical pressure oscillation near the material interface is successfully avoided.• It can accurately model violent hydrodynamic slamming problems by properly dealing the crucial compressibility effects of fluid.• It can also model complex hull cavitation problems in addition to incipient cavitation.• The hydrocode is successfully accelerated on the GPU by a speed up over 60x. AbstractThis paper presents a GPU based compressible multiphase hydrocode for modelling violent hydrodynamic impacts under harsh conditions such as slamming and underwater explosion. An effort is made to extend a one-dimensional five-equation reduced model (Kapila et al., Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations, Phys. Fluids, 2001, Vol.13, 3002 -3024) to compute three-dimensional hydrodynamic impact problems on modern graphics hardware. In order to deal with free-surface problems such as water waves, gravitational terms, which are initially absent from the original model, are now considered and included in the governing equations. A third-order finite volume based MUSCL scheme is applied to discretise the integral form of the governing equations. The numerical flux across a mesh cell face is estimated by means of the HLLC approximate Riemann solver. The serial CPU program is firstly parallelised on multi-core CPUs with the OpenMP programming model and then further accelerated on many-core graphics processing units (GPUs) using the CUDA C programming language.To balance memory usage, computing efficiency and accuracy on multi-and many-core processors, a mixture of single and double precision floating-point operations is implemented. The most important data like conservative flow variables are handled with double-precision dynamic arrays, whilst all the other variables/arrays like fluxes, residual and source terms are treated in single precision. Several benchmark test cases including water-air shock tubes, one-dimensional liquid cavitation tube, dam break, 2D cylindrical underwater explosion near a planar rigid wall, 3D spherical explosion in a rigid cylindrical container and water entry of a 3D rigid flat plate have been calculated using the present approach. The obtained results agree well with experiments, exact solutions and other independent numerical computations. This demonstrates the capability of the present approach to deal with not only violent free-surface impact problems but also hull cavitation associated with underwater explosions. Performance analysis reveals that the running time cost of numerical simulations is dramatically reduced by use of GPUs with much less consumption of electrical energy than on the CPU.

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Section: Performance Analysissupporting

confidence: 76%

A GPU based compressible multiphase hydrocode for modelling violent hydrodynamic impact problems

Causon

Qian

et al. 2015

Computers & Fluids

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“…According to these results, second-order accuracy can be considered an upper bound in quadratic FPM approximations, with the attainable value depending on the characteristics of the specific problem being solved. Numerical investigations confirm these results in practical application cases; see grid convergence analyses in [56] and the examples in Section 5.…”

Section: Accuracy Of the Fpm Approximationsupporting

confidence: 59%

“…As a result, collocation techniques become a natural choice to discretize the problem equations. Further details about the FPM approximation and the global and local domain discretization techniques employed are given in [51,52].…”

Section: /26mentioning

confidence: 99%

A-posteriori error estimation for the finite point method with applications to compressible flow

et al. 2017

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Aquesta és una còpia de la versió author's final draft d'un article publicat a la revista Computational mechanics. Abstract. An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations. This approximation is calculated from the discrete nodal differential residuals using a reconstructed solution field on a modified stencil of points. Both the error estimation methodology and the flow solution scheme are implemented using the Finite Point Method, a meshless technique enabling higher-order approximations and reconstruction procedures on general unstructured discretizations. The performance of the proposed error indicator is studied and applications to adaptive grid refinement are presented.

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“…And, similar meshless discretization technique such as the finitevolume particle method (FVPM) has been employed for convergence analysis for compressible as well as incompressible flows [37,38]. In addition, the validations of the finite particle method have been conducted through classical benchmark tests with exact analytical solutions, in terms of accuracy as well as conservation properties [39,40].…”

Section: Introductionmentioning

confidence: 99%

Grid‐Free Modelling Based on the Finite Particle Method for Incompressible Viscous Flow Problems

Chang

et al. 2019

Shock and Vibration

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In this paper, we present a grid-free modelling based on the finite particle method for the numerical simulation of incompressible viscous flows. Numerical methods of interest are meshless Lagrangian finite point scheme by the application of the projection method for the incompressibility of the Navier–Stokes flow equations. The moving least squares method is introduced for approximating spatial derivatives in a meshless context. The pressure Poisson equation with Neumann boundary condition is solved by the finite particle method in which the fluid domain is discretized by a finite number of particles. Also, a continuous particle management has to be done to prevent particles from moving into configurations problematic for a numerical approximation. With the proposed finite particle technique, problems associated with the viscous free surface flow which contains the study on the liquid sloshing in tanks with low volumetric fluid type, solitary waves movement, and interaction with a vertical wall in numerical flume as well as the vortex patterns of the ship rolling damping are circumvented. These numerical models are investigated to validate the presented grid-free methodology. The results have revealed the efficiency and stability of the finite particle method which could be well handled with the incompressible viscous flow problems.

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Comparative accuracy and performance assessment of the finite point method in compressible flow problems

Cited by 12 publications

References 17 publications

A GPU based compressible multiphase hydrocode for modelling violent hydrodynamic impact problems

A GPU based compressible multiphase hydrocode for modelling violent hydrodynamic impact problems

A-posteriori error estimation for the finite point method with applications to compressible flow

Grid‐Free Modelling Based on the Finite Particle Method for Incompressible Viscous Flow Problems

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