arXiv subjects

Maciej Matyka

Publications and source records attributed to Maciej Matyka.

28 records · Page 2Linked to original sources

arXiv2012

Complete PISO and SIMPLE solvers on Graphics Processing Units

We implemented the pressure-implicit with splitting of operators (PISO) and semi-implicit method for pressure-linked equations (SIMPLE) solvers of the Navier-Stokes equations on Fermi-class graphics processing units (GPUs) using the CUDA technology. We also introduced a new format of sparse matrices optimized for performing elementary CFD operations, like gradient or divergence discretization, on GPUs. We verified the validity of the implementation on several standard, steady and unsteady problems. Computational effciency of the GPU implementation was examined by comparing its double precision run times with those of essentially the same algorithms implemented in OpenFOAM. The results show that a GPU (Tesla C2070) can outperform a server-class 6-core, 12-thread CPU (Intel Xeon X5670) by a factor of 4.2.

cs.DC↗

arXiv2012

How to Calculate Tortuosity Easily?

Tortuosity is one of the key parameters describing the geometry and transport properties of porous media. It is defined either as an average elongation of fluid paths or as a retardation factor that measures the resistance of a porous medium to the flow. However, in contrast to a retardation factor, an average fluid path elongation is difficult to compute numerically and, in general, is not measurable directly in experiments. We review some recent achievements in bridging the gap between the two formulations of tortuosity and discuss possible method of numerical and an experimental measurements of the tortuosity directly from the fluid velocity field.

physics.flu-dyn↗

arXiv2012

Wall Orientation and Shear Stress in the Lattice Boltzmann Model

The wall shear stress is a quantity of profound importance for clinical diagnosis of artery diseases. The lattice Boltzmann is an easily parallelizable numerical method of solving the flow problems, but it suffers from errors of the velocity field near the boundaries which leads to errors in the wall shear stress and normal vectors computed from the velocity. In this work we present a simple formula to calculate the wall shear stress in the lattice Boltzmann model and propose to compute wall normals, which are necessary to compute the wall shear stress, by taking the weighted mean over boundary facets lying in a vicinity of a wall element. We carry out several tests and observe an increase of accuracy of computed normal vectors over other methods in two and three dimensions. Using the scheme we compute the wall shear stress in an inclined and bent channel fluid flow and show a minor influence of the normal on the numerical error, implying that that the main error arises due to a corrupted velocity field near the staircase boundary. Finally, we calculate the wall shear stress in the human abdominal aorta in steady conditions using our method and compare the results with a standard finite volume solver and experimental data available in the literature. Applications of our ideas in a simplified protocol for data preprocessing in medical applications are discussed.

physics.comp-ph↗

arXiv2011

Hydraulic tortuosity in arbitrary porous media flow

Tortuosity ($T$) is a parameter describing an average elongation of fluid streamlines in a porous medium as compared to free flow. In this paper several methods of calculating this quantity from lengths of individual streamlines are compared and their weak and strong features are discussed. An alternative method is proposed, which enables one to calculate $T$ directly from the fluid velocity field, without the need of determining streamlines, which greatly simplifies determination of tortuosity in complex geometries, including those found in experiments or 3D computer models. Numerical results obtained with this method suggest that (a) the hydraulic tortuosity of an isotropic fibrous medium takes on the form $T = 1 + p\sqrt{1-ϕ}$, where $ϕ$ is the porosity and $p$ is a constant and (b) the exponent controlling the divergence of $T$ with the system size at percolation threshold is related to an exponent describing the scaling of the most probable traveling length at bond percolation.

physics.flu-dyn↗

arXiv2009

Numerical modeling of fluid flow through porous media (Modelowanie numeryczne transportu plynow przez osrodki porowate)

The aim of the thesis is to present and analyze two particular problems of transport in porous media flow. The first of them is related to the process of saturation of porous building materials. Recently, M. Küntz and P. Lavalée, using a computer model of this process, have concluded that the anomalous diffusion assumption is correct. In this thesis I present an alternative explanation of this results without any refer to anomalous diffusion. The second part of the thesis covers the numerical analysis of the tortuosity of the flow -- one of a very interesting physical macroscopic variables characterizing transport in porous media. (in Polish)

physics.comp-ph↗

arXiv2009

Finite-size anisotropy in statistically uniform porous media

Anisotropy of the permeability tensor in statistically uniform porous media of sizes used in typical computer simulations is studied. Although such systems are assumed to be isotropic by default, we show that de facto their anisotropic permeability can give rise to significant changes of transport parameters such as permeability and tortuosity. The main parameter controlling the anisotropy is $a/L$, being the ratio of the obstacle to system size. Distribution of the angle $α$ between the external force and the volumetric fluid stream is found to be approximately normal, and the standard deviation of $α$ is found to decay with the system size as $(a/L)^{d/2}$, where $d$ is the space dimensionality. These properties can be used to estimate both anisotropy-related statistical errors in large-scale simulations and the size of the representative elementary volume.

physics.flu-dyn↗

arXiv2008

Tortuosity-porosity relation in the porous media flow

We study numerically the tortuosity--porosity relation in a microscopic model of a porous medium arranged as a collectin of freely overlapping squares. It is demonstrated that the finite-size effects and the discretization errors, which were ignored in previous studies, may cause significant underestimation of tortuosity. The simple tortuosity calculation method proposed here eliminates the need for using complicated, weighted averages. The numerical results presented here are in good agreement with an empirical relation between tortuosity ($T$) and porosity ($ϕ$) given by $T-1\propto \lnϕ$, that was found by others experimentally in granule packings and sediments. This relation can be also written as $T-1\propto R S/ϕ$ with $R$ and $S$ denoting the hydraulic radius of granules and the specific surface area, respectively.

physics.flu-dyn↗

arXiv2007

Spreading of a density front in the Küntz-Lavallée model of porous media

We analyze spreading of a density front in the Küntz-Lavallée model of porous media. In contrast to previous studies, where unusual properties of the front were attributed to anomalous diffusion, we find that the front evolution is controlled by normal diffusion and hydrodynamic flow, the latter being responsible for apparent enhancement of the front propagation speed. Our finding suggests that results of several recent experiments on porous media, where anomalous diffusion was reported based on the density front propagation analysis, should be reconsidered to verify the role of a fluid flow.

physics.flu-dyn↗

arXiv2004

Solution to two-dimensional Incompressible Navier-Stokes Equations with SIMPLE, SIMPLER and Vorticity-Stream Function Approaches. Driven-Lid Cavity Problem: Solution and Visualization

In that report solution to incompressible Navier - Stokes equations in non - dimensional form will be presented. Standard fundamental methods: SIMPLE, SIMPLER (SIMPLE Revised) and Vorticity-Stream function approach are compared and results of them are analyzed for standard CFD test case - Drived Cavity flow. Different aspect ratios of cavity and different Reynolds numbers are studied.

physics.flu-dyn↗

arXiv2003

Incompressible Couette Flow

This project work report provides a full solution of simplified Navier Stokes equations for The Incompressible Couette Problem. The well known analytical solution to the problem of incompressible couette is compared with a numerical solution. In that paper, I will provide a full solution with simple C code instead of MatLab or Fortran codes, which are known. For discrete problem formulation, implicit Crank-Nicolson method was used. Finally, the system of equation (tridiagonal) is solved with both Thomas and simple Gauss Method. Results of both methods are compared.

physics.comp-ph↗