I am an artist, scientist, entrepreneur, and programmer interested in high-performance computing, computational fluid dynamics (CFD), algorithmic artwork, geographic information systems, and digital cartography. I expect to contribute to pages presenting information on vortexes, vortex methods, and computational tools for fluid dynamics, but also pages mentioning heights of buildings and mountains. Here are the pages that I've touched so far, most recent first:
My credentials for commenting come from a PhD in Aerospace Engineering (University of Michigan, 2006) and a series of papers on vortex sheet and particle methods over the last 5 years available from my web site. In addition, I am the founder and principal of terrain and urban data-processing and printing companies TinyMtn and MiniCity.Art.
(also Lagrangian Vortex Particle Method (LVPM), Free Vortex Method (FVM), Discrete Vortex Method (DVM))
sssVortex methods are novel computational fluids dynamics (CFD) methods that use Lagrangian discretizations of vorticity to allow computers to perform predictive simulations of fluid phenomena for science and engineering. More traditional CFD methods use Eulerian (fixed) spatial discretizations and velocity-pressure variables, which come with specific computational disadvantages including numerical instability and complex volumetric meshing. Vortex methods address these disadvantages at the expense of increased computational cost per time step and decreased generality.
Lord Kelvin refers to vortex atoms in 1867 [1], but not in the sense of fluid dynamics. A.R. Low first expressed the idea of tracking vorticity in 1928 [2], but the first calculations using vortex methods were accomplished by Rosenhead [3] [4] in 1930-1. A long delay between these early efforts ended in 1959 with the repetition of Rosenhead's experiment by Birkhoff and Fisher [5], and then numerical experiments by Tung and Ting in 1967 [6]. Significant research began to appear in the 1970s, three-dimensional vortex methods and parallelization efforts dominated research in the 1980s, and the breadth of computational techniques and applications for vortex methods has been growing rapidly since the 1990s. [7]
Incompressible assumption eliminates
Starts with taking the curl of the Navier-Stokes equations.
Two major method types exist for determining the velocity field from a distribution of vorticity. One begins with the Biot-Savart law, and the other involves solving the Laplace equation within a Particle-in-cell method.
Vortex methods encompass a wide range of computational, numerical, and algorithmic techniques. This section will present the various classifications of historical and modern vortex methods.
Both the earliest and the most capable current vortex methods solvers discretize vorticity onto discrete Lagrangian particles. Still, many vortex methods use alternative discretizations such as filaments and sheets. Each has advantages and disadvantages, though researchers have been focusing most effort recently on particle vortex methods.
Particles have become the most common vortex method discretization technique because they are more capable of accounting for the variety of terms in the vorticity equation. Adapting a particle distribution...
Vortex filament methods benefit from Kelvin's observations that the circulation of a vortex line does not change along its length, and it does not end in free space---only on a solid body. This eliminates the need to calculate the stretching component of the vorticity equation and explains why vortex filament methods were the first three-dimensional vortex simulations. Adaptation of the filaments is accomplished by splitting long segments in two parts and placing the new node either at the geometric center of the old segment or along a spline connecting the original nodes. Adaptation cannot easily occur along any non-tangential direction without extra connectivity information.
Vorticity very commonly enters a flow at interfaces between two fluids, or as the result of shedding from a solid body, lending support to vortex methods based on sheet discretizations. In two dimensions these sheets are continuous linear or higher-order connected segments. In three dimensions sheets are described by connected meshes of triangles or quadrilaterals. Adaptation in the two sheet-tangent directions can take a variety of forms, depending on the element shape. Adaptation in the sheet-normal direction is generally not attempted.
A list of major researchers who have contributed to vortex methods in the past three decades includes, but is not limited to: A. Chorin, G.H. Cottet, A. Gharakhani, A. Ghoniem, P. Koumoutsakos, R. Krasny, A. Leonard, J. Strickland, G. Winckelmans.
I am an artist, scientist, entrepreneur, and programmer interested in high-performance computing, computational fluid dynamics (CFD), algorithmic artwork, geographic information systems, and digital cartography. I expect to contribute to pages presenting information on vortexes, vortex methods, and computational tools for fluid dynamics, but also pages mentioning heights of buildings and mountains. Here are the pages that I've touched so far, most recent first:
My credentials for commenting come from a PhD in Aerospace Engineering (University of Michigan, 2006) and a series of papers on vortex sheet and particle methods over the last 5 years available from my web site. In addition, I am the founder and principal of terrain and urban data-processing and printing companies TinyMtn and MiniCity.Art.
(also Lagrangian Vortex Particle Method (LVPM), Free Vortex Method (FVM), Discrete Vortex Method (DVM))
sssVortex methods are novel computational fluids dynamics (CFD) methods that use Lagrangian discretizations of vorticity to allow computers to perform predictive simulations of fluid phenomena for science and engineering. More traditional CFD methods use Eulerian (fixed) spatial discretizations and velocity-pressure variables, which come with specific computational disadvantages including numerical instability and complex volumetric meshing. Vortex methods address these disadvantages at the expense of increased computational cost per time step and decreased generality.
Lord Kelvin refers to vortex atoms in 1867 [1], but not in the sense of fluid dynamics. A.R. Low first expressed the idea of tracking vorticity in 1928 [2], but the first calculations using vortex methods were accomplished by Rosenhead [3] [4] in 1930-1. A long delay between these early efforts ended in 1959 with the repetition of Rosenhead's experiment by Birkhoff and Fisher [5], and then numerical experiments by Tung and Ting in 1967 [6]. Significant research began to appear in the 1970s, three-dimensional vortex methods and parallelization efforts dominated research in the 1980s, and the breadth of computational techniques and applications for vortex methods has been growing rapidly since the 1990s. [7]
Incompressible assumption eliminates
Starts with taking the curl of the Navier-Stokes equations.
Two major method types exist for determining the velocity field from a distribution of vorticity. One begins with the Biot-Savart law, and the other involves solving the Laplace equation within a Particle-in-cell method.
Vortex methods encompass a wide range of computational, numerical, and algorithmic techniques. This section will present the various classifications of historical and modern vortex methods.
Both the earliest and the most capable current vortex methods solvers discretize vorticity onto discrete Lagrangian particles. Still, many vortex methods use alternative discretizations such as filaments and sheets. Each has advantages and disadvantages, though researchers have been focusing most effort recently on particle vortex methods.
Particles have become the most common vortex method discretization technique because they are more capable of accounting for the variety of terms in the vorticity equation. Adapting a particle distribution...
Vortex filament methods benefit from Kelvin's observations that the circulation of a vortex line does not change along its length, and it does not end in free space---only on a solid body. This eliminates the need to calculate the stretching component of the vorticity equation and explains why vortex filament methods were the first three-dimensional vortex simulations. Adaptation of the filaments is accomplished by splitting long segments in two parts and placing the new node either at the geometric center of the old segment or along a spline connecting the original nodes. Adaptation cannot easily occur along any non-tangential direction without extra connectivity information.
Vorticity very commonly enters a flow at interfaces between two fluids, or as the result of shedding from a solid body, lending support to vortex methods based on sheet discretizations. In two dimensions these sheets are continuous linear or higher-order connected segments. In three dimensions sheets are described by connected meshes of triangles or quadrilaterals. Adaptation in the two sheet-tangent directions can take a variety of forms, depending on the element shape. Adaptation in the sheet-normal direction is generally not attempted.
A list of major researchers who have contributed to vortex methods in the past three decades includes, but is not limited to: A. Chorin, G.H. Cottet, A. Gharakhani, A. Ghoniem, P. Koumoutsakos, R. Krasny, A. Leonard, J. Strickland, G. Winckelmans.