A new asynchronous methodology for modeling of physical systems: breaking the curse of courant condition

Abstract

Computer simulation of many important complex physical systems has reached a plateau because most conventional techniques are ill equipped to deal with the multi-scale nature of such systems. The traditional technique to simulate physical systems modeled by partial differential equations consists of breaking the simulation domain into a spatial grid and then advancing the state of the system synchronously at regular discrete time intervals. This socalled time-driven (or time-stepped) simulation (TDS) has inherent inefficiencies such as the time step restriction imposed by a global CFL (Courant-Friedrichs-Levy) condition. There is ongoing research on introducing local time refinement (local versus global CFL) within the time-stepped methodology. Here, we propose an entirely different (asynchronous) simulation methodology which uses the spatial grid but the time advance is based on a discrete event-driven (as opposed to time-driven) approach. This new technique immediately offers several major advantages over TDS. First, it allows each part of the simulation, that is the individual cells in case of fluid simulations and individual particles within a cell in case of particle simulations, to evolve based on their own physically determined time scales. Second, unlike in the TDS where the system is updated faithfully in time based on a pre-selected user specified time step, here the role of time step is replaced by a threshold for local state change. In our technique, individual parts of the global simulation state are updated on a ''need-to-be-done-only'' basis. Individual parts of the simulation domain set their own time scales for change, which may vary in space as well as during the run. In a particle-in-cell (PIC) simulation, DES enables a self-adjusting temporal mesh for each simulation entity down to assigning an individual time step to each particle. In this paper, we illustrate this new technique via the example of a spacecraft charging in a neutral plasma due to injection of a charged beam particle from its surface and compare its performance with the traditional techniques. We find that even in one-dimension, the new DES technology can be more than 300 times faster than the traditional TDS. Aside from sheer performance advantages, the real power of this technique is in its inherent ability to adapt to the spatial inhomogeneity of the problem. This enables building intelligent algorithms where interaction of simulation entities (e.g., cells, particles) follow elementary rules set by the

Asynchronous Event-Driven Particle Algorithms

“…For example, in PIC (particlein-cell) algorithms for plasma simulation, the cells are used to solve for background electric fields using FFT transforms [19]. In DSMC, the algorithm stochastically collides pairs of particles that are in the same cell.…”

Simulation of a Large Wildfire in a Coupled Fire-Atmosphere Model

“…A new marker is dynamically added if two markers are farther than d and deleted if closer than d/2. The Discrete Event Simulation (DES) time scheme permits one to apply the Courant-Friedrichs-Lewy (CFL) constraint to each segment at each marker update and consequently updating more frequently areas where the interface is the most active (in an approach similar to [35]). In DES, each simulation element, node, marker or sub-model must compute its optimal local time step and schedule its future update as events in a shared and time-sorted timetable.…”

CellLab-CTS 2015: continuous-time stochastic cellular automaton modeling using Landlab

“…In order to place events in the correct time sequence, we adopt an approach that is commonly used in other types of discrete-event simulations (e.g., Karimabadi et al, 2005;Karimabadi, 2006, 2007), in which future events are recorded in a queue that sorts them according to time of occurrence. When a new event needs to be scheduled, we create an event object, which stores the location of the transition, the time at which it is scheduled to occur, and the new node states.…”

“…When a transition oc- curs at one of the four pairs, the other three scheduled transitions immediately become invalid, and their scheduled transitions should be ignored when they are popped from the event queue. To handle this situation, whenever an event is scheduled, its transition time is also recorded separately in the transition-time array (as is done in the discrete-event algorithms of Karimabadi et al, 2005and Omelchenko and Karimabadi, 2006. Then, each time an event is popped from the event queue, it is executed only if its transition time matches the entry in the transition-time array.…”