Validation and Verification Case Study of Various Vlasov Solvers - - PowerPoint PPT Presentation

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AFTC PA Release# 15007, 1 6 Jan 2015 Validation and Verification Case Study of Various Vlasov Solvers David Bilyeu Air Force Research Lab, In-space Propulsion, NRC Post-doc (formerly) January 20, 2015 Distribution A: For Public Release;

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SLIDE 1

Validation and Verification Case Study of Various Vlasov Solvers

David Bilyeu

Air Force Research Lab, In-space Propulsion, NRC Post-doc (formerly)

January 20, 2015

AFTC PA Release# 15007, 16 Jan 2015

Distribution A: For Public Release; Distribution Unlimited 1/12

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SLIDE 2

Overview

Goal

DEVELOP A HYBRID KINETIC/FLUID SOLVER THAT CAN EFFICIENTLY SIMULATE A WIDE RANGE OF PLASMA DEVICES AND CONDITIONS

Distribution A: For Public Release; Distribution Unlimited 2/12

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SLIDE 3

Overview

Goal

DEVELOP A HYBRID KINETIC/FLUID SOLVER THAT CAN EFFICIENTLY SIMULATE A WIDE RANGE OF PLASMA DEVICES AND CONDITIONS

1 Overview 2 Motivation 3 Vlasov Verification and Validation

Distribution A: For Public Release; Distribution Unlimited 2/12

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SLIDE 4

Overview

Kinetic/Particle description of Gases

  • Under normal conditions the

distribution of the particles (VDF) is known.

  • If an outside force/field

perturbs the distribution it will relax back to a Maxwellian distribution in a finite amount of time.

  • Ratio of the characteristic length to the Mean Free path (ℓ)

◮ e.g. ∆x/ℓ 10, STP 68nm, Rocket engine 5 nm, Hall Thruster 1 cm

  • Ratio of the characteristic time scale to the Relaxation time (τ)

◮ e.g. ∆t/τ 5 Distribution A: For Public Release; Distribution Unlimited 3/12

slide-5
SLIDE 5

Overview

Kinetic/Particle description of Gases

  • Under normal conditions the

distribution of the particles (VDF) is known.

  • If an outside force/field

perturbs the distribution it will relax back to a Maxwellian distribution in a finite amount of time.

  • Ratio of the characteristic length to the Mean Free path (ℓ)

◮ e.g. ∆x/ℓ 10, STP 68nm, Rocket engine 5 nm, Hall Thruster 1 cm

  • Ratio of the characteristic time scale to the Relaxation time (τ)

◮ e.g. ∆t/τ 5 Distribution A: For Public Release; Distribution Unlimited 3/12

slide-6
SLIDE 6

Overview

Kinetic/Particle description of Gases

  • Under normal conditions the

distribution of the particles (VDF) is known.

  • If an outside force/field

perturbs the distribution it will relax back to a Maxwellian distribution in a finite amount of time.

✵ ✵✳✺ ✶ ✶✳✺ ✷ ✷✳✺ ✵ ✶✵✵✵ ✷✵✵✵ ✸✵✵✵ Pr♦❜✐❜✐❧✐t② ✭✶✵✵✵✮ ❙♣❡❡❞ ◆✷ ❍❡ ❖✷

  • Ratio of the characteristic length to the Mean Free path (ℓ)

◮ e.g. ∆x/ℓ 10, STP 68nm, Rocket engine 5 nm, Hall Thruster 1 cm

  • Ratio of the characteristic time scale to the Relaxation time (τ)

◮ e.g. ∆t/τ 5 Distribution A: For Public Release; Distribution Unlimited 3/12

slide-7
SLIDE 7

Overview

Kinetic/Particle description of Gases

  • Under normal conditions the

distribution of the particles (VDF) is known.

  • If an outside force/field

perturbs the distribution it will relax back to a Maxwellian distribution in a finite amount of time.

✵ ✵✳✶ ✵✳✷ ✵✳✸ ✵✳✹ ✵✳✺ ✵✳✻ ✵✳✼ ✵ ✷✵✵✵ ✹✵✵✵ Pr♦❜✐❜✐❧✐t② ✭✶✵✵✵✮ ❙♣❡❡❞

  • Ratio of the characteristic length to the Mean Free path (ℓ)

◮ e.g. ∆x/ℓ 10, STP 68nm, Rocket engine 5 nm, Hall Thruster 1 cm

  • Ratio of the characteristic time scale to the Relaxation time (τ)

◮ e.g. ∆t/τ 5 Distribution A: For Public Release; Distribution Unlimited 3/12

slide-8
SLIDE 8

Overview

Kinetic/Particle description of Gases

  • Under normal conditions the

distribution of the particles (VDF) is known.

  • If an outside force/field

perturbs the distribution it will relax back to a Maxwellian distribution in a finite amount of time.

✵ ✵✳✶ ✵✳✷ ✵✳✸ ✵✳✹ ✵✳✺ ✵✳✻ ✵✳✼ ✵ ✷✵✵✵ ✹✵✵✵ Pr♦❜✐❜✐❧✐t② ✭✶✵✵✵✮ ❙♣❡❡❞

  • Ratio of the characteristic length to the Mean Free path (ℓ)

◮ e.g. ∆x/ℓ 10, STP 68nm, Rocket engine 5 nm, Hall Thruster 1 cm

  • Ratio of the characteristic time scale to the Relaxation time (τ)

◮ e.g. ∆t/τ 5 Distribution A: For Public Release; Distribution Unlimited 3/12

slide-9
SLIDE 9

Overview

Kinetic/Particle description of Gases

  • Under normal conditions the

distribution of the particles (VDF) is known.

  • If an outside force/field

perturbs the distribution it will relax back to a Maxwellian distribution in a finite amount of time.

✵ ✵✳✶ ✵✳✷ ✵✳✸ ✵✳✹ ✵✳✺ ✵✳✻ ✵✳✼ ✵ ✷✵✵✵ ✹✵✵✵ Pr♦❜✐❜✐❧✐t② ✭✶✵✵✵✮ ❙♣❡❡❞

  • Ratio of the characteristic length to the Mean Free path (ℓ)

◮ e.g. ∆x/ℓ 10, STP 68nm, Rocket engine 5 nm, Hall Thruster 1 cm

  • Ratio of the characteristic time scale to the Relaxation time (τ)

◮ e.g. ∆t/τ 5 Distribution A: For Public Release; Distribution Unlimited 3/12

slide-10
SLIDE 10

Overview

Kinetic/Particle description of Gases

  • Under normal conditions the

distribution of the particles (VDF) is known.

  • If an outside force/field

perturbs the distribution it will relax back to a Maxwellian distribution in a finite amount of time.

✵ ✵✳✶ ✵✳✷ ✵✳✸ ✵✳✹ ✵✳✺ ✵✳✻ ✵✳✼ ✵ ✷✵✵✵ ✹✵✵✵ Pr♦❜✐❜✐❧✐t② ✭✶✵✵✵✮ ❙♣❡❡❞

  • Ratio of the characteristic length to the Mean Free path (ℓ)

◮ e.g. ∆x/ℓ 10, STP 68nm, Rocket engine 5 nm, Hall Thruster 1 cm

  • Ratio of the characteristic time scale to the Relaxation time (τ)

◮ e.g. ∆t/τ 5 Distribution A: For Public Release; Distribution Unlimited 3/12

slide-11
SLIDE 11

Overview

Kinetic/Particle description of Gases

  • Under normal conditions the

distribution of the particles (VDF) is known.

  • If an outside force/field

perturbs the distribution it will relax back to a Maxwellian distribution in a finite amount of time.

✵ ✵✳✶ ✵✳✷ ✵✳✸ ✵✳✹ ✵✳✺ ✵✳✻ ✵✳✼ ✵ ✷✵✵✵ ✹✵✵✵ Pr♦❜✐❜✐❧✐t② ✭✶✵✵✵✮ ❙♣❡❡❞

  • Ratio of the characteristic length to the Mean Free path (ℓ)

◮ e.g. ∆x/ℓ 10, STP 68nm, Rocket engine 5 nm, Hall Thruster 1 cm

  • Ratio of the characteristic time scale to the Relaxation time (τ)

◮ e.g. ∆t/τ 5 Distribution A: For Public Release; Distribution Unlimited 3/12

slide-12
SLIDE 12

Overview

Kinetic/Particle description of Gases

  • Under normal conditions the

distribution of the particles (VDF) is known.

  • If an outside force/field

perturbs the distribution it will relax back to a Maxwellian distribution in a finite amount of time.

✵ ✵✳✶ ✵✳✷ ✵✳✸ ✵✳✹ ✵✳✺ ✵✳✻ ✵✳✼ ✵ ✷✵✵✵ ✹✵✵✵ Pr♦❜✐❜✐❧✐t② ✭✶✵✵✵✮ ❙♣❡❡❞

  • Ratio of the characteristic length to the Mean Free path (ℓ)

◮ e.g. ∆x/ℓ 10, STP 68nm, Rocket engine 5 nm, Hall Thruster 1 cm

  • Ratio of the characteristic time scale to the Relaxation time (τ)

◮ e.g. ∆t/τ 5 Distribution A: For Public Release; Distribution Unlimited 3/12

slide-13
SLIDE 13

Overview

Kinetic/Particle description of Gases

  • Under normal conditions the

distribution of the particles (VDF) is known.

  • If an outside force/field

perturbs the distribution it will relax back to a Maxwellian distribution in a finite amount of time.

✵ ✵✳✶ ✵✳✷ ✵✳✸ ✵✳✹ ✵✳✺ ✵✳✻ ✵✳✼ ✵ ✷✵✵✵ ✹✵✵✵ Pr♦❜✐❜✐❧✐t② ✭✶✵✵✵✮ ❙♣❡❡❞

  • Ratio of the characteristic length to the Mean Free path (ℓ)

◮ e.g. ∆x/ℓ 10, STP 68nm, Rocket engine 5 nm, Hall Thruster 1 cm

  • Ratio of the characteristic time scale to the Relaxation time (τ)

◮ e.g. ∆t/τ 5 Distribution A: For Public Release; Distribution Unlimited 3/12

slide-14
SLIDE 14

Overview

Types of Solvers

Eulerian (MHD) v f

  • Numerically

inexpensive

  • Mature technology
  • Straight forward

algorithms

  • VDF is fixed

Distribution A: For Public Release; Distribution Unlimited 4/12

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SLIDE 15

Overview

Types of Solvers

Eulerian (MHD) v f Vlasov v f

  • Numerically

inexpensive

  • Mature technology
  • Straight forward

algorithms

  • VDF is fixed
  • VDF is smooth
  • Relatively easy to

implement

  • Becomes VERY

Numerically expensive in multi-D

Distribution A: For Public Release; Distribution Unlimited 4/12

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SLIDE 16

Overview

Types of Solvers

Eulerian (MHD) v f Vlasov v f Particle (PIC) v

  • Numerically

inexpensive

  • Mature technology
  • Straight forward

algorithms

  • VDF is fixed
  • VDF is smooth
  • Relatively easy to

implement

  • Becomes VERY

Numerically expensive in multi-D

  • Numerically Efficient

in multi-D

  • Mature technology
  • Very noisy
  • Difficult to optimize
  • Numerically expensive

as density increases

Distribution A: For Public Release; Distribution Unlimited 4/12

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SLIDE 17

Motivation

Problems that we Simulate

  • Spacecraft-Plume

interaction

  • Thruster Performance
  • Laser Plasma Interaction

Distribution A: For Public Release; Distribution Unlimited 5/12

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SLIDE 18

Motivation

Problems that we Simulate

  • Spacecraft-Plume

interaction

◮ Will the thruster hinder

  • perations?
  • Thruster Performance
  • Laser Plasma Interaction

Distribution A: For Public Release; Distribution Unlimited 5/12

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SLIDE 19

Motivation

Problems that we Simulate

  • Spacecraft-Plume

interaction

◮ Will the thruster hinder

  • perations?
  • Thruster Performance
  • Laser Plasma Interaction

Distribution A: For Public Release; Distribution Unlimited 5/12

slide-20
SLIDE 20

Motivation

Problems that we Simulate

  • Spacecraft-Plume

interaction

◮ Will the thruster hinder

  • perations?
  • Thruster Performance

◮ What happens around

the thruster?

  • Laser Plasma Interaction

Distribution A: For Public Release; Distribution Unlimited 5/12

slide-21
SLIDE 21

Motivation

Problems that we Simulate

  • Spacecraft-Plume

interaction

◮ Will the thruster hinder

  • perations?
  • Thruster Performance

◮ What happens around

the thruster?

◮ How will the thruster

behave in space?

  • Laser Plasma Interaction

Distribution A: For Public Release; Distribution Unlimited 5/12

slide-22
SLIDE 22

Motivation

Problems that we Simulate

  • Spacecraft-Plume

interaction

◮ Will the thruster hinder

  • perations?
  • Thruster Performance

◮ What happens around

the thruster?

◮ How will the thruster

behave in space?

  • Laser Plasma Interaction

Distribution A: For Public Release; Distribution Unlimited 5/12

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SLIDE 23

Motivation

Problems that we Simulate

  • Spacecraft-Plume

interaction

◮ Will the thruster hinder

  • perations?
  • Thruster Performance

◮ What happens around

the thruster?

◮ How will the thruster

behave in space?

  • Laser Plasma Interaction

◮ Particle acceleration Distribution A: For Public Release; Distribution Unlimited 5/12

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SLIDE 24

Motivation

Problems that we Simulate

  • Spacecraft-Plume

interaction

◮ Will the thruster hinder

  • perations?
  • Thruster Performance

◮ What happens around

the thruster?

◮ How will the thruster

behave in space?

  • Laser Plasma Interaction

◮ Particle acceleration ◮ Medical imaging Distribution A: For Public Release; Distribution Unlimited 5/12

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SLIDE 25

Motivation

Problems that we Simulate

  • Spacecraft-Plume

interaction

◮ Will the thruster hinder

  • perations?
  • Thruster Performance

◮ What happens around

the thruster?

◮ How will the thruster

behave in space?

  • Laser Plasma Interaction

◮ Particle acceleration ◮ Medical imaging ◮ Plasma diagnostics Distribution A: For Public Release; Distribution Unlimited 5/12

slide-26
SLIDE 26

Motivation

Problems that we Simulate

  • Spacecraft-Plume

interaction

◮ Will the thruster hinder

  • perations?
  • Thruster Performance

◮ What happens around

the thruster?

◮ How will the thruster

behave in space?

  • Laser Plasma Interaction

◮ Particle acceleration ◮ Medical imaging ◮ Plasma diagnostics

PIC

Distribution A: For Public Release; Distribution Unlimited 5/12

slide-27
SLIDE 27

Motivation

Problems that we Simulate

  • Spacecraft-Plume

interaction

◮ Will the thruster hinder

  • perations?
  • Thruster Performance

◮ What happens around

the thruster?

◮ How will the thruster

behave in space?

  • Laser Plasma Interaction

◮ Particle acceleration ◮ Medical imaging ◮ Plasma diagnostics

PIC PIC and Vlasov

Distribution A: For Public Release; Distribution Unlimited 5/12

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SLIDE 28

Motivation

Problems that we Simulate

  • Spacecraft-Plume

interaction

◮ Will the thruster hinder

  • perations?
  • Thruster Performance

◮ What happens around

the thruster?

◮ How will the thruster

behave in space?

  • Laser Plasma Interaction

◮ Particle acceleration ◮ Medical imaging ◮ Plasma diagnostics

PIC PIC and Vlasov Vlasov and Two- Fluid MHD

Distribution A: For Public Release; Distribution Unlimited 5/12

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SLIDE 29

Motivation

A Hybrid Simulation

  • Traditionally . . .

◮ Plasma: Ions treated as particles (PIC) and electrons treated as a

fluid

  • New approach, domain decomposition

Distribution A: For Public Release; Distribution Unlimited 6/12

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SLIDE 30

Motivation

A Hybrid Simulation

  • Traditionally . . .

◮ Plasma: Ions treated as particles (PIC) and electrons treated as a

fluid

  • New approach, domain decomposition

Distribution A: For Public Release; Distribution Unlimited 6/12

slide-31
SLIDE 31

Motivation

A Hybrid Simulation

  • Traditionally . . .

◮ Plasma: Ions treated as particles (PIC) and electrons treated as a

fluid

  • New approach, domain decomposition

Distribution A: For Public Release; Distribution Unlimited 6/12

slide-32
SLIDE 32

Motivation

A Hybrid Simulation

  • Traditionally . . .

◮ Plasma: Ions treated as particles (PIC) and electrons treated as a

fluid

  • New approach, domain decomposition

Distribution A: For Public Release; Distribution Unlimited 6/12

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SLIDE 33

Motivation

Numerical Considerations

  • Numerical solvers

◮ Continuum method; Two-temperature MHD, Hall MHD,

Multi-fluid MHD, . . .

◮ Continuous kinetic model; Vlasov ◮ Discrete kinetic model; PIC

  • Inter-solver communication, e.g. how to get two different solvers

to communicate with each other

  • When to switch to another solver
  • Logistics, how to handle various solvers in the same framework

Distribution A: For Public Release; Distribution Unlimited 7/12

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SLIDE 34

Motivation

Numerical Considerations

  • Numerical solvers

◮ Continuum method; Two-temperature MHD, Hall MHD,

Multi-fluid MHD, . . .

◮ Continuous kinetic model; Vlasov ◮ Discrete kinetic model; PIC

  • Inter-solver communication, e.g. how to get two different solvers

to communicate with each other

  • When to switch to another solver
  • Logistics, how to handle various solvers in the same framework

Distribution A: For Public Release; Distribution Unlimited 7/12

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SLIDE 35

Vlasov Verification and Validation

Overview

Test Cases

  • Verification

◮ Weak and strong Landau dampening

  • Validation

◮ Collisionless Electrostatic Shock

Solvers

  • Semi-Lagrangian

◮ WENO reconstruction, Qiu, Shu, and Christlieb ◮ DG reconstruction, Rossmanith and Seal

  • Finite Volume/Element

◮ MP-WENO ◮ CESE Distribution A: For Public Release; Distribution Unlimited 8/12

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SLIDE 36

Vlasov Verification and Validation

Weak Landau Dampening

Distribution A: For Public Release; Distribution Unlimited 9/12

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SLIDE 37

Vlasov Verification and Validation

Weak Landau Dampening

Distribution A: For Public Release; Distribution Unlimited 9/12

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SLIDE 38

Vlasov Verification and Validation

Strong Landau Dampening

Distribution A: For Public Release; Distribution Unlimited 10/12

slide-39
SLIDE 39

Vlasov Verification and Validation

Strong Landau Dampening

Distribution A: For Public Release; Distribution Unlimited 10/12

slide-40
SLIDE 40

Vlasov Verification and Validation

Collisionless Electrostatic Shock

Distribution A: For Public Release; Distribution Unlimited 11/12

slide-41
SLIDE 41

Vlasov Verification and Validation

Collisionless Electrostatic Shock

Distribution A: For Public Release; Distribution Unlimited 11/12

slide-42
SLIDE 42

Vlasov Verification and Validation

Collisionless Electrostatic Shock

Distribution A: For Public Release; Distribution Unlimited 11/12

slide-43
SLIDE 43

Vlasov Verification and Validation

Collisionless Electrostatic Shock

Distribution A: For Public Release; Distribution Unlimited 11/12

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SLIDE 44

Vlasov Verification and Validation

Conclusion and Future Work

  • Vlasov is a real alternative to PIC for kinetic simulations
  • The behavior of the Vlasov solvers in simple test cases may not be

reflected in physical simulation

  • Still need to determine where the mass goes
  • Implement a collisional operator such as BGK or FP

Distribution A: For Public Release; Distribution Unlimited 12/12