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

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; Distribution Unlimited 1/12

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

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

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

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

Overview Kinetic/Particle description of Gases • Under normal conditions the ✷✳✺ distribution of the particles Pr♦❜✐❜✐❧✐t② ✭✶✵✵✵✮ ◆✷ (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

Overview Kinetic/Particle description of Gases • Under normal conditions the ✵✳✼ distribution of the particles Pr♦❜✐❜✐❧✐t② ✭✶✵✵✵✮ ✵✳✻ (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

Overview Kinetic/Particle description of Gases • Under normal conditions the ✵✳✼ distribution of the particles Pr♦❜✐❜✐❧✐t② ✭✶✵✵✵✮ ✵✳✻ (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

Overview Kinetic/Particle description of Gases • Under normal conditions the ✵✳✼ distribution of the particles Pr♦❜✐❜✐❧✐t② ✭✶✵✵✵✮ ✵✳✻ (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

Overview Kinetic/Particle description of Gases • Under normal conditions the ✵✳✼ distribution of the particles Pr♦❜✐❜✐❧✐t② ✭✶✵✵✵✮ ✵✳✻ (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

Overview Kinetic/Particle description of Gases • Under normal conditions the ✵✳✼ distribution of the particles Pr♦❜✐❜✐❧✐t② ✭✶✵✵✵✮ ✵✳✻ (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

Overview Kinetic/Particle description of Gases • Under normal conditions the ✵✳✼ distribution of the particles Pr♦❜✐❜✐❧✐t② ✭✶✵✵✵✮ ✵✳✻ (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

Overview Kinetic/Particle description of Gases • Under normal conditions the ✵✳✼ distribution of the particles Pr♦❜✐❜✐❧✐t② ✭✶✵✵✵✮ ✵✳✻ (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

Overview Types of Solvers Eulerian (MHD) f v • Numerically inexpensive • Mature technology • Straight forward algorithms • VDF is fixed Distribution A: For Public Release; Distribution Unlimited 4/12

Overview Types of Solvers Eulerian (MHD) Vlasov f f v v • Numerically • VDF is smooth inexpensive • Relatively easy to • Mature technology implement • Straight forward • Becomes VERY algorithms Numerically expensive • VDF is fixed in multi-D Distribution A: For Public Release; Distribution Unlimited 4/12

Overview Types of Solvers Eulerian (MHD) Particle (PIC) Vlasov f f v v v • Numerically • VDF is smooth • Numerically Efficient inexpensive in multi-D • Relatively easy to • Mature technology • Mature technology implement • Straight forward • Becomes VERY • Very noisy algorithms Numerically expensive • Difficult to optimize • VDF is fixed in multi-D • Numerically expensive as density increases Distribution A: For Public Release; Distribution Unlimited 4/12

Motivation Problems that we Simulate • Spacecraft-Plume interaction • Thruster Performance • Laser Plasma Interaction Distribution A: For Public Release; Distribution Unlimited 5/12

Motivation Problems that we Simulate • Spacecraft-Plume interaction ◮ Will the thruster hinder operations? • Thruster Performance • Laser Plasma Interaction Distribution A: For Public Release; Distribution Unlimited 5/12

Motivation Problems that we Simulate • Spacecraft-Plume interaction ◮ Will the thruster hinder operations? • Thruster Performance • Laser Plasma Interaction Distribution A: For Public Release; Distribution Unlimited 5/12