User talk:Homa18/sandbox

In the 1990s, the use of computer simulations as a virtual environment to model complex physical systems was gaining momentum, driven to a large extent by increase in computational power. A common simulation technique consists of dividing the simulation domain into a computational grid, initializing the system and then updating the state of the system over time.

At the time, computer simulation techniques were being looked into with an eye towards applications in plasma physics, such as fusion, space physics such as space weather, among others. A common characteristic among these applications is that different parts of the system evolve at different rates in time. An ideal algorithm would intelligently adapt the timestep at each computational grid based on local conditions to achieve a desired accuracy. As it turns out, this is a very challenging task for the algorithms. The standard techniques, generally called time-stepped based, faithfully update the system at equal timesteps, leading to great inefficiency, and putting realistic modeling of many systems out of reach.

Imagine simulating car traffic on the freeway. It would be quite wasteful to update the simulation as often in the bumper-to-bumper traffic part of the freeway, where there is slow change over time, as in the part where cars are traveling at full speed. The common approach to address this problem has been to create patches in the simulation with finer spatial grids and then update the patches at smaller timesteps. This leads to well-known numerical issues but that is the best that was available. And it is even more problematical to have such algorithms adaptively move the patches in time (e.g., have the fine resolution patch follow the traffic jams in time).

Having reached the conclusion that, the wide spread use of time-stepped approach is fundamentally flawed for simulating temporally inhomogeneous systems, alternatives were looked into. In the process a technique, called discrete event simulation, was found which was being used in applications where the evolution of system occurs in distinct events and the system is assumed to have no change in between the events. Applications include video games, battle field simulation, traffic flow modeling, among others. For example, in the battle field simulation, the event of interest may be whether the tank hits its target and all other aspects such as the detailed motion tracking of the tank could be ignored.

This technique, which is action-based, is completely different than the time-stepped methodology where the dynamics of the system is continuously tracked over time. The question was whether it was feasible to adapt the discrete event methodology for simulation of problems that were traditionally addressed by time-stepped approaches. It took about a year before there was proof of concept, which was published in 2005 (Karimabadi et al., 2005). As it often happens in science, new breakthroughs and fundamentally different approaches, encounter a certain degree of resistance from the scientific community. But eventually with more proof points the resistance dissipates and turns into acceptance. The technique has since been developed further (e.g., Omelchenko and Karimabadi, 2006, 2007, 2012a, 2012b). It has found applications in other domains such as modeling of wildfires, oil reservoirs, computational fluid dynamics, plasma discharges, among others. The algorithm provides significant improvements in speed, and accuracy compared to standard techniques. It also exhibits better stability properties. Even today, it remains the only algorithm of its type where it self-adaptively changes the timestep on each computational grid.

Read full article and watch movies here: https://homakarimabadi.blogspot.com/

Omelchenko Y.A. and H. Karimabadi, Spontaneous generation of a sheared plasma rotation in a field-reversed -pinch discharge, Phys. Rev. Lett. 109, 065004, 2012a. Omelchenko, Y.A. and H. Karimabadi, HYPERS: A Unidimensional Asynchronous Framework for Multiscale Hybrid Simulations, J. Comp. Phys. 231,1766-1780, 2012b. Omelchenko, Y.A. and H. Karimabadi, A Time-Accurate Explicit Multiscale Technique for Gas Dynamics, J. Comp. Phys. 226 (1): 282-300, 2007. Omelchenko Y.A. and H. Karimabadi, Self-adaptive time integration of flux-conservative equations with sources, J. Comp. Phys. 216, 179-194, 2006. Karimabadi H., J. Driscoll, Y.A. Omelchenko, and N. Omidi, A new asynchronous methodology of modeling of physical systems, J. Comp. Phys. 205( 2), 755-775, 2005.

Homa Karimabadi 23:00, 20 June 2018 (UTC)