Damping Options - Revision history

Nairnj: /* PIC Damping */

2026-04-12T19:40:11Z

PIC Damping

← Older revision		Revision as of 19:40, 12 April 2026
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	<math> \vec v_{p}^{(n+1)} = \beta \vec v_{p,FLIP}^{(n+1)} + (1-\beta)\vec v_{p,PIC}^{(n+1)} </math>		<math> \vec v_{p}^{(n+1)} = \beta \vec v_{p,FLIP}^{(n+1)} + (1-\beta)\vec v_{p,PIC}^{(n+1)} </math>

	If this ~~method~~ also mixes fraction β of standard FLIP position update with fraction (1-β) of PIC position update (although original reference incorrectly did not mix position updates<ref name="Diz"/>), it provides one option for controlling the amount of damping. [[NairnMPM]] provides a similar feature, but rather than mix FLIP and PIC on each time step, it intersperses FLIP time steps with PIC time steps. If a PIC time step is done every n<sup>th</sup> time step, it is nearly the same as a simulation with β=(n-1)/n. To create simulations with periodic PIC, add a [[PeriodicXPIC Custom Task]] to you simulation.		If this approach also mixes fraction β of standard FLIP position update with fraction (1-β) of PIC position update (although original reference incorrectly did not mix position updates<ref name="Diz"/>), it provides one option for controlling the amount of damping. [[NairnMPM]] provides a similar feature, but rather than mix FLIP and PIC on each time step, it intersperses FLIP time steps with PIC time steps. If a PIC time step is done every n<sup>th</sup> time step, it is nearly the same as a simulation with β=(n-1)/n. To create simulations with periodic PIC, add a [[PeriodicXPIC Custom Task]] to you simulation.

	An alternative to mixing FLIP with PIC is to use two new advanced methods that enhance PIC-style updates to minimize or eliminate their dissipation. The two methods are called [[FMPM Features\|FMPM(k) and XPIC(k)]] for FMPM or XPIC of order k. FMPM(1) and XPIC(1) are two similar versions of PIC but sample simulations show to FMPM(1) is better than XPIC(1) and both are much better then a PIC method that omits PIC damping in the position update. Orders greater than one provide new methods that can stabilize simulations without causing too much dissipation. These two methods are added to simulations by using the [[PeriodicXPIC Custom Task]].		An alternative to mixing FLIP with PIC is to use two new advanced methods that enhance PIC-style updates to minimize or eliminate their dissipation. The two methods are called [[FMPM Features\|FMPM(k) and XPIC(k)]] for FMPM or XPIC of order k. FMPM(1) and XPIC(1) are two similar versions of PIC but sample simulations show to FMPM(1) is better than XPIC(1) and both are much better then a PIC method that omits PIC damping in the position update. Orders greater than one provide new methods that can stabilize simulations without causing too much dissipation. These two methods are added to simulations by using the [[PeriodicXPIC Custom Task]].

Nairnj: /* PIC Damping */

2026-04-12T19:39:22Z

PIC Damping

← Older revision		Revision as of 19:39, 12 April 2026
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	* By implementing PIC as a damping mechanism, it became clear how to modify the position update in PIC as well.<ref name="cutting"/> Some early proposals to use PIC (or to mix a fraction PIC with FLIP) used PIC update for velocity but retained the FLIP update for position.<ref name="Diz"/> The above position update addresses that issue and greatly improves particle displacement results in simulations using PIC.<ref name="cutting"/> Also note that standard damping terms in the position update are second order, but because PIC damping is inversely proportional to Δ''t'', the PIC damping term is a first order term in the position update.		* By implementing PIC as a damping mechanism, it became clear how to modify the position update in PIC as well.<ref name="cutting"/> Some early proposals to use PIC (or to mix a fraction PIC with FLIP) used PIC update for velocity but retained the FLIP update for position.<ref name="Diz"/> The above position update addresses that issue and greatly improves particle displacement results in simulations using PIC.<ref name="cutting"/> Also note that standard damping terms in the position update are second order, but because PIC damping is inversely proportional to Δ''t'', the PIC damping term is a first order term in the position update.

	A drawback of PIC damping is ~~typcially that~~ it damps too much. It can work well is quasi-static problems, but often damps too much in dynamic problems. A paper on using MPM for animation<ref name="Diz"/> suggested that simulations could be improved by modifying the velocity update to include a fraction β of standard FLIP style MPM velocity updates and a fraction (1-β) of PIC style updates:		A drawback of PIC damping is it usually damps too much. It can work well is quasi-static problems, but often damps too much in dynamic problems. A paper on using MPM for animation<ref name="Diz"/> suggested that simulations could be improved by modifying the velocity update to include a fraction β of standard FLIP style MPM velocity updates and a fraction (1-β) of PIC style updates:

Nairnj: /* PIC Damping */

2026-04-12T19:38:13Z

PIC Damping

← Older revision		Revision as of 19:38, 12 April 2026
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	* It provides insight and justification for adding PIC. The PIC damping term is related to the extrapolation error between particle velocity and extrapolated grid velocity. This error will be large in elements that contain particles with widely varying velocity (as sometimes happens in MPM simulations) and small in areas with rather uniform velocity. Thus PIC damping will selectively damp out regions with large velocity variations and have little affect on regions with smooth velocities.		* It provides insight and justification for adding PIC. The PIC damping term is related to the extrapolation error between particle velocity and extrapolated grid velocity. This error will be large in elements that contain particles with widely varying velocity (as sometimes happens in MPM simulations) and small in areas with rather uniform velocity. Thus PIC damping will selectively damp out regions with large velocity variations and have little affect on regions with smooth velocities.
	* By implementing PIC as a damping mechanism, it became clear how to modify the position update in PIC as well.<ref name="cutting"/> Some early proposals to use PIC (or to mix a fraction PIC with FLIP) used PIC update for velocity but retained the FLIP update for position<ref name="Diz"/>. The above position update addresses that issue and greatly improves particle displacement results in simulations using PIC<ref name="cutting"/>. Also note that standard damping terms in the position update are second order, but because PIC damping is inversely proportional to Δ''t'', the PIC damping term is a first order term in the position update.		* By implementing PIC as a damping mechanism, it became clear how to modify the position update in PIC as well.<ref name="cutting"/> Some early proposals to use PIC (or to mix a fraction PIC with FLIP) used PIC update for velocity but retained the FLIP update for position.<ref name="Diz"/> The above position update addresses that issue and greatly improves particle displacement results in simulations using PIC.<ref name="cutting"/> Also note that standard damping terms in the position update are second order, but because PIC damping is inversely proportional to Δ''t'', the PIC damping term is a first order term in the position update.

	A drawback of PIC damping is typcially that it damps too much. It can work well is quasi-static problems, but often damps too much in dynamic problems. A paper on using MPM for animation<ref name="Diz"/> suggested that simulations could be improved by modifying the velocity update to include a fraction β of standard FLIP style MPM velocity updates and a fraction (1-β) of PIC style updates:		A drawback of PIC damping is typcially that it damps too much. It can work well is quasi-static problems, but often damps too much in dynamic problems. A paper on using MPM for animation<ref name="Diz"/> suggested that simulations could be improved by modifying the velocity update to include a fraction β of standard FLIP style MPM velocity updates and a fraction (1-β) of PIC style updates:

Nairnj: /* PIC Damping */

2026-04-12T19:35:50Z

PIC Damping

← Older revision		Revision as of 19:35, 12 April 2026
Line 70:		Line 70:
	If this method also mixes fraction β of standard FLIP position update with fraction (1-β) of PIC position update (although original reference incorrectly did not mix position updates<ref name="Diz"/>), it provides one option for controlling the amount of damping. [[NairnMPM]] provides a similar feature, but rather than mix FLIP and PIC on each time step, it intersperses FLIP time steps with PIC time steps. If a PIC time step is done every n<sup>th</sup> time step, it is nearly the same as a simulation with β=(n-1)/n. To create simulations with periodic PIC, add a [[PeriodicXPIC Custom Task]] to you simulation.		If this method also mixes fraction β of standard FLIP position update with fraction (1-β) of PIC position update (although original reference incorrectly did not mix position updates<ref name="Diz"/>), it provides one option for controlling the amount of damping. [[NairnMPM]] provides a similar feature, but rather than mix FLIP and PIC on each time step, it intersperses FLIP time steps with PIC time steps. If a PIC time step is done every n<sup>th</sup> time step, it is nearly the same as a simulation with β=(n-1)/n. To create simulations with periodic PIC, add a [[PeriodicXPIC Custom Task]] to you simulation.

	An alternative to mixing FLIP with PIC is to use two new advanced methods that enhance PIC-style updates to minimize or eliminate their dissipation. The two methods are called [[FMPM Features\|FMPM(k) and (XPIC(k)]] for FMPM or XPIC of order k. FMPM(1) and XPIC(1) are two similar versions of PIC ~~(note that~~ FMPM(1) is better than XPIC(1)). Orders greater than one provide new methods that can stabilize simulations without causing too much dissipation. These two methods are added to simulations by using the [[PeriodicXPIC Custom Task]].		An alternative to mixing FLIP with PIC is to use two new advanced methods that enhance PIC-style updates to minimize or eliminate their dissipation. The two methods are called [[FMPM Features\|FMPM(k) and XPIC(k)]] for FMPM or XPIC of order k. FMPM(1) and XPIC(1) are two similar versions of PIC but sample simulations show to FMPM(1) is better than XPIC(1) and both are much better then a PIC method that omits PIC damping in the position update. Orders greater than one provide new methods that can stabilize simulations without causing too much dissipation. These two methods are added to simulations by using the [[PeriodicXPIC Custom Task]].

	== Damping Commands ==		== Damping Commands ==

Nairnj: /* PIC Damping */

2026-04-12T19:31:52Z

PIC Damping

← Older revision		Revision as of 19:31, 12 April 2026
Line 68:		Line 68:
	<math> \vec v_{p}^{(n+1)} = \beta \vec v_{p,FLIP}^{(n+1)} + (1-\beta)\vec v_{p,PIC}^{(n+1)} </math>		<math> \vec v_{p}^{(n+1)} = \beta \vec v_{p,FLIP}^{(n+1)} + (1-\beta)\vec v_{p,PIC}^{(n+1)} </math>

	If this method also mixes fraction β of standard FLIP fraction (1-β) of PIC position ~~updates~~ (although original reference did not mix position ~~options~~<ref name="Diz"/>) it provides ~~and options~~ for controlling the amount of damping. [[NairnMPM]] provides a similar feature, but rather than mix FLIP and PIC on each time step, it intersperses FLIP time steps with PIC time steps. If a PIC time step is done every n<sup>th</sup> time step, it is nearly the same as a simulation with β=(n-1)/n. To create simulations with periodic PIC, add a [[PeriodicXPIC Custom Task]] to you simulation.		If this method also mixes fraction β of standard FLIP position update with fraction (1-β) of PIC position update (although original reference incorrectly did not mix position updates<ref name="Diz"/>), it provides one option for controlling the amount of damping. [[NairnMPM]] provides a similar feature, but rather than mix FLIP and PIC on each time step, it intersperses FLIP time steps with PIC time steps. If a PIC time step is done every n<sup>th</sup> time step, it is nearly the same as a simulation with β=(n-1)/n. To create simulations with periodic PIC, add a [[PeriodicXPIC Custom Task]] to you simulation.

	An alternative to mixing FLIP with PIC is to use two new advanced methods that enhance PIC-style updates to minimize or eliminate their dissipation. The two methods are called [[FMPM Features\|FMPM(k) and (XPIC(k)]] for FMPM or XPIC of order k. FMPM(1) and XPIC(1) are two similar versions of PIC (note that FMPM(1) is better than XPIC(1)). Orders greater than one provide new methods that can stabilize simulations without causing too much dissipation. These two methods are added to simulations by using the [[PeriodicXPIC Custom Task]].		An alternative to mixing FLIP with PIC is to use two new advanced methods that enhance PIC-style updates to minimize or eliminate their dissipation. The two methods are called [[FMPM Features\|FMPM(k) and (XPIC(k)]] for FMPM or XPIC of order k. FMPM(1) and XPIC(1) are two similar versions of PIC (note that FMPM(1) is better than XPIC(1)). Orders greater than one provide new methods that can stabilize simulations without causing too much dissipation. These two methods are added to simulations by using the [[PeriodicXPIC Custom Task]].

Nairnj: /* PIC Damping */

2026-04-12T19:29:03Z

PIC Damping

← Older revision		Revision as of 19:29, 12 April 2026
Line 63:		Line 63:
	* By implementing PIC as a damping mechanism, it became clear how to modify the position update in PIC as well.<ref name="cutting"/> Some early proposals to use PIC (or to mix a fraction PIC with FLIP) used PIC update for velocity but retained the FLIP update for position<ref name="Diz"/>. The above position update addresses that issue and greatly improves particle displacement results in simulations using PIC<ref name="cutting"/>. Also note that standard damping terms in the position update are second order, but because PIC damping is inversely proportional to Δ''t'', the PIC damping term is a first order term in the position update.		* By implementing PIC as a damping mechanism, it became clear how to modify the position update in PIC as well.<ref name="cutting"/> Some early proposals to use PIC (or to mix a fraction PIC with FLIP) used PIC update for velocity but retained the FLIP update for position<ref name="Diz"/>. The above position update addresses that issue and greatly improves particle displacement results in simulations using PIC<ref name="cutting"/>. Also note that standard damping terms in the position update are second order, but because PIC damping is inversely proportional to Δ''t'', the PIC damping term is a first order term in the position update.

	A drawback of PIC damping is typcially that it damps too much. It can work well is quasi-static problems, but often damps too much in an dynamic problems. A paper on using MPM for animation<ref name="Diz"/> suggested that simulations could be improved by modifying the velocity update to include a fraction β of standard FLIP style MPM velocity updates and a fraction (1-β) of PIC style updates:		A drawback of PIC damping is typcially that it damps too much. It can work well is quasi-static problems, but often damps too much in dynamic problems. A paper on using MPM for animation<ref name="Diz"/> suggested that simulations could be improved by modifying the velocity update to include a fraction β of standard FLIP style MPM velocity updates and a fraction (1-β) of PIC style updates:

Nairnj: /* PIC Damping */

2026-04-12T19:28:41Z

PIC Damping

← Older revision		Revision as of 19:28, 12 April 2026
Line 61:		Line 61:

	* It provides insight and justification for adding PIC. The PIC damping term is related to the extrapolation error between particle velocity and extrapolated grid velocity. This error will be large in elements that contain particles with widely varying velocity (as sometimes happens in MPM simulations) and small in areas with rather uniform velocity. Thus PIC damping will selectively damp out regions with large velocity variations and have little affect on regions with smooth velocities.		* It provides insight and justification for adding PIC. The PIC damping term is related to the extrapolation error between particle velocity and extrapolated grid velocity. This error will be large in elements that contain particles with widely varying velocity (as sometimes happens in MPM simulations) and small in areas with rather uniform velocity. Thus PIC damping will selectively damp out regions with large velocity variations and have little affect on regions with smooth velocities.
	* By implementing PIC as a damping mechanism, it became clear how to modify the position update in PIC as well.<ref name="cutting"/> Some early proposals to use PIC (or to mix a fraction PIC with FLIP) used PIC update for velocity but retained the FLIP update for position<ref name="Diz"/>. The above position update addresses that issue and greatly improves particle displacement results in simulations using PIC<ref name="cutting"/>. Also note that ~~the~~ damping terms in the position update are second order, but because PIC damping is inversely proportional to Δ''t'', the PIC damping ~~terms become~~ first order ~~terms~~ in the position update.		* By implementing PIC as a damping mechanism, it became clear how to modify the position update in PIC as well.<ref name="cutting"/> Some early proposals to use PIC (or to mix a fraction PIC with FLIP) used PIC update for velocity but retained the FLIP update for position<ref name="Diz"/>. The above position update addresses that issue and greatly improves particle displacement results in simulations using PIC<ref name="cutting"/>. Also note that standard damping terms in the position update are second order, but because PIC damping is inversely proportional to Δ''t'', the PIC damping term is a first order term in the position update.

	A drawback of PIC damping is typcially that it damps too much. It can work well is quasi-static problems, but often damps too much in an dynamic problems. A paper on using MPM for animation<ref name="Diz"/> suggested that simulations could be improved by modifying the velocity update to include a fraction β of standard FLIP style MPM velocity updates and a fraction (1-β) of PIC style updates:		A drawback of PIC damping is typcially that it damps too much. It can work well is quasi-static problems, but often damps too much in an dynamic problems. A paper on using MPM for animation<ref name="Diz"/> suggested that simulations could be improved by modifying the velocity update to include a fraction β of standard FLIP style MPM velocity updates and a fraction (1-β) of PIC style updates:

Nairnj: /* PIC Damping */

2026-04-12T19:27:16Z

PIC Damping

← Older revision		Revision as of 19:27, 12 April 2026
Line 56:		Line 56:


	PIC Damping = <math>\frac{\vec v_{g\to p}^{(n)~~}-\vec V_{p~~}}{\Delta t}</math>		PIC Damping = <math>\frac{\vec V_{p}-\vec v_{g\to p}^{(n)}}{\Delta t}</math>

	This damping interpretion of PIC leads to two significant improvements for the use of PIC in simulations:		This damping interpretion of PIC leads to two significant improvements for the use of PIC in simulations:

Nairnj: /* PIC Damping */

2026-04-12T19:26:37Z

PIC Damping

← Older revision		Revision as of 19:26, 12 April 2026
Line 56:		Line 56:


	PIC Damping = <math>\frac{~~\vec V_{p}~~\vec v_{g\to p}^{(n)}}{\Delta t}</math>		PIC Damping = <math>\frac{\vec v_{g\to p}^{(n)}-\vec V_{p}}{\Delta t}</math>

	This damping interpretion of PIC leads to two significant improvements for the use of PIC in simulations:		This damping interpretion of PIC leads to two significant improvements for the use of PIC in simulations:

Nairnj: /* PIC Damping */

2026-04-12T19:25:16Z

PIC Damping

← Older revision		Revision as of 19:25, 12 April 2026
Line 53:		Line 53:
	<math> \vec V_p^{(n+1)} = \vec V_p^{(n)} + \biggl(\vec a_{g\to p}^{(n)} - \left(\alpha_g-{1\over \Delta t}\right) \vec v_{g\to p}^{(n)} - \left(\alpha_p+{1\over \Delta t}\right) \vec V_{p}^{(n)}\biggr)\Delta t </math>		<math> \vec V_p^{(n+1)} = \vec V_p^{(n)} + \biggl(\vec a_{g\to p}^{(n)} - \left(\alpha_g-{1\over \Delta t}\right) \vec v_{g\to p}^{(n)} - \left(\alpha_p+{1\over \Delta t}\right) \vec V_{p}^{(n)}\biggr)\Delta t </math>

	This damping ~~view~~ of PIC leads to two significant improvements for the use of PIC in simulations:		The extra damping created by adopting PIC methods are seen to be


			PIC Damping = <math>\frac{\vec V_{p}\vec v_{g\to p}^{(n)}}{\Delta t}</math>

			This damping interpretion of PIC leads to two significant improvements for the use of PIC in simulations:

	* It provides insight and justification for adding PIC. The PIC damping term is related to the extrapolation error between particle velocity and extrapolated grid velocity. This error will be large in elements that contain particles with widely varying velocity (as sometimes happens in MPM simulations) and small in areas with rather uniform velocity. Thus PIC damping will selectively damp out regions with large velocity variations and have little affect on regions with smooth velocities.		* It provides insight and justification for adding PIC. The PIC damping term is related to the extrapolation error between particle velocity and extrapolated grid velocity. This error will be large in elements that contain particles with widely varying velocity (as sometimes happens in MPM simulations) and small in areas with rather uniform velocity. Thus PIC damping will selectively damp out regions with large velocity variations and have little affect on regions with smooth velocities.