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The Ghost Fluid Method

The Ghost Fluid Method. Ron Fedkiw. Applications. Isobaric Fix - Fedkiw, Marquina, Merriman Compressible Flow Contact Discontinuities - Fedkiw, Aslam, Merriman, Osher Deflagrations , Detonations , & Shocks - Fedkiw, Aslam, Xu Viscosity - Fedkiw , Liu , Kang , Gibou

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The Ghost Fluid Method

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  1. TheGhostFluidMethod Ron Fedkiw CIT ASCI Alliance Program

  2. Applications IsobaricFix - Fedkiw, Marquina, Merriman CompressibleFlow Contact Discontinuities- Fedkiw, Aslam, Merriman, Osher Deflagrations,Detonations, & Shocks - Fedkiw, Aslam, Xu Viscosity - Fedkiw, Liu, Kang, Gibou Pulsating Detonation - Huang, Aslam, Karagozian, Fedkiw PoissonEquation & Hele-ShawFlow - Liu, Fedkiw, Kang, Sideris IncompressibleFlow Contact Discontinuities - Kang, Fedkiw, Liu Flames - Nguyen, Fedkiw, Kang StefanProblem - Fedkiw, Merriman, Chen Compressible\Incompressible - Caiden, Anderson, Fedkiw Eulerian\Lagrangian- Fedkiw, Shepherd, Hung, Arienti CIT ASCI Alliance Program

  3. Isobaric Fix for wall overheating Numerical Method appropriate pressure and velocity inappropriate entropy Inviscid Flow - no boundary condition for entropy - we are free to extrapolate entropy Isobaric Fix Density Errors Patrick Hung CIT ASCI Alliance Program

  4. Contact Discontinuity pressure & velocity are continuous entropy is discontinuous Numerical Dissipation Extrapolate Entropy CIT ASCI Alliance Program

  5. Ghost Fluid Method - 2 phase flow Tait EOS & Gamma Law Gas CIT ASCI Alliance Program

  6. Level Set Methods keep track of the interface properties with the signed distance function interface location - two separate fluids - unit normal - curvature - moving the interface - signed distance function - extrapolation - continuous and interface velocity extrapolated variable CIT ASCI Alliance Program

  7. Capturing the Boundary Conditions Create a fictitious Ghost Fluid Continuous Variables - copy them over from the real fluid in a node by node fashion (pressure and normal velocity) Discontinuous Variables - extrapolate them from the fluid on the other side of the interface (entropy and tangential velocity) no slip boundary condition - tangential velocity is continuous thermal heat conduction - temperature is continuous CIT ASCI Alliance Program

  8. Shock Contact Interaction Tariq Aslam, LANL interface (sharp) shock initial interface location rarefaction CIT ASCI Alliance Program

  9. Computational Mesh Polygonal Lagrangian Mesh Cartesian Eulerian Mesh Real Nodes Ghost Nodes CIT ASCI Alliance Program

  10. Solution Triple U - classical solution I - interface representation B - boundary conditions Eulerian Code U- mass, momentum, and energy @ real nodes I - the level set function on the Cartesian mesh B - mass, momentum, and energy @ ghost nodes Lagrangian Code U - mass, velocity, and pressure on the Lagrangian mesh I - polygonal interface representation B - pressure (possibly velocity) at points on the interface CIT ASCI Alliance Program

  11. Numerical Summary dt=min(dt,dt) (U,I,B) (U,I,B) Eulerian Code Lagrangian Code level set I U I U I interpolation B discontinuous continuous B CIT ASCI Alliance Program

  12. Solid-Fluid Coupling Patrick Hung CIT ASCI Alliance Program

  13. Eulerian-Lagrangian Coupling (1D) • Single shock wave propagating down “shock-tube”. • Eulerian computational domain covers the entire tube. • Lagrangian mesh covers the right most part of the tube. • Eulerian-Lagrangian coupling using GFM. • Boundary conditions: Open/Closed CIT ASCI Alliance Program

  14. Numerical Methods. • Eulerian computation based on Ron Fedkiw’s code. • Perfect gas EOS. • Completely independent of the Amrita environment. • Uses a rectangular (non-AMR) cartesian mesh. • Lagrangian computation. • Artificial Viscosity (1D) (D.J. Benson) • Entire program scripted using MATLAB. • GFM • Eulerian-Lagragian: Pressure at the interface. • Lagrangian-Eulerian: Position and velocity of the interface. CIT ASCI Alliance Program

  15. Eulerian-Lagrangian Coupling (1D) • Initial Pressure Profile and Domain Specification. CIT ASCI Alliance Program

  16. Eulerian/Lagrangian (1D). Case 1. • Right end fixed. • Density in target (Lagrangian) twenty times lower. Pressure Profile CIT ASCI Alliance Program

  17. Eulerian/Lagrangian (1D). Case 2 • Right end free. • Density in target (Lagrangian) twenty times lower. Pressure Profile and x-t Diagram CIT ASCI Alliance Program

  18. Eulerian/Lagrangian Coupling (2D) • Problem setup. CIT ASCI Alliance Program

  19. Eulerian/Lagrangian Coupling (2D) • 1D mass elements used to represent the solid tube. Density Contours CIT ASCI Alliance Program

  20. Future Directions • Migration to Python. • 1D examples performed with MATLAB as the engine driving Eulerian code written in C, and Lagrangian code in MATLAB. • 2D examples in Fortran. • Virtual Testing Facility. • Detonation tube and the corner turning problem. • Integration with the Solid Mechanics group to replace the current simplistic Lagrangian component. • Parallelization. CIT ASCI Alliance Program

  21. MG Eos and Ghost Fluid Method Marco Arienti CIT ASCI Alliance Program

  22. HMX HMX M Roadmap EoS for HE Shock tube with GFM Shock in HE hitting mass + spring with GFM K CIT ASCI Alliance Program

  23. Material characterization • Mie-Grüneisen Equation of State: • Linear Up-us shock relation: • G, c0, s CIT ASCI Alliance Program

  24. Inert b-HMX: shock tube • P1=105 , r1=1891, P2= 2.109 , r2=2200 [SI units] density pressure velocity CIT ASCI Alliance Program

  25. Inert Kel-F: shock tube experiment • P1=105 , r1=2133, P2= 80.109 , r2=2633 [SI units] CIT ASCI Alliance Program

  26. Inert b-HMX & mass-spring system • P1=1.0 105 Pa (right green)r1= 1891. Kg/m3 • P2= 9.8109 Pa (left green)r2= 2400. Kg/m3 • solidEulerian code: • ENO method • 3rd order Total Variation Diminishing Runge-Kutta • density based GFM • Interface gr: from solid to fluid CIT ASCI Alliance Program

  27. Inert b-HMX & mass-spring system • Case 1: Ks=1014 N/m, Ms=103 Kg, Pg = 105 Pa pressure density CIT ASCI Alliance Program

  28. Inert b-HMX & mass-spring system • Case 2: Ks=1012 N/m, Ms=5.102 Kg, Pg = 105 Pa velocity density CIT ASCI Alliance Program

  29. K HMX M HMX L HMX Future directions Shock in reacting HE hitting mass + spring with GFM Shock in reacting HE hitting Lagrangean solid with GFM Integration with 2D Lagrangean boundary CIT ASCI Alliance Program

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