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In computational fluid dynamics, the projection method, also called Chorin's projection method, is an effective means of numerically solving time-dependent incompressible fluid-flow problems. It was originally introduced by Alexandre Chorin in 1967 [ 1 ] [ 2 ] as an efficient means of solving the incompressible Navier-Stokes equations .
Based on the idea of "providing the local velocity field around the material point to the background grid by transferring the material point's velocity gradient," Jiang et al. (2015 [14]) proposed the APIC method. In this method, the particle velocity is locally affine, mathematically expressed as: [14]
Michael J. Black is an American-German computer scientist currently working in Tübingen, Germany. He is a founding director at the Max Planck Institute for Intelligent Systems where he leads the Perceiving Systems Department in research focused on computer vision, machine learning, and computer graphics.
The mass imbalance is often also used for control of the outer loop. The name of this class of methods stems from the fact that the correction of the velocity field is computed through the pressure-field. The discretization of this is typically done with either the finite element method or the finite volume method. With the latter, one might ...
[34] [35] [36] Powered by pseudospectral methods, Ross created a user-friendly set of objects that required no knowledge of his theory to run DIDO. This work was used in on pseudospectral methods for solving optimal control problems. [37] DIDO is used for solving optimal control problems in aerospace applications, [38] [39] search theory, [40 ...
Dykstra's algorithm is a method that computes a point in the intersection of convex sets, and is a variant of the alternating projection method (also called the projections onto convex sets method). In its simplest form, the method finds a point in the intersection of two convex sets by iteratively projecting onto each of the convex set; it ...
A related, and more commonly used algorithm is the velocity Verlet algorithm, [5] similar to the leapfrog method, except that the velocity and position are calculated at the same value of the time variable (leapfrog does not, as the name suggests). This uses a similar approach, but explicitly incorporates velocity, solving the problem of the ...
The method is sometimes called minor loop synthesis in college textbooks, [1] [2] some government documents. [3] The method is suitable for design by graphical methods and was used before digital computers became available. In World War 2 this method was used to design gun laying control systems. [4] It is still used now, but not always ...