1. Progress Report on SPARTAN Chamber Dynamics Simulation Code Farrokh Najmabadi and Zoran Dragojlovic HAPL Meeting February 5-6, 2004 Georgia Institute of Technology Electronic copy: http://aries.ucsd.edu/najmabadi/TALKS UCSD IFE Web Site: http://aries.ucsd.edu/IFE

2.  2-D Transient Compressible Navier-Stokes Equations.  Second order Godunov method, for capturing strong shocks.  Diffusive terms (conductivity, viscosity) can depend on local state variables.  Adaptive Mesh Refinement employed to secure the uniform accuracy throughout the fluid domain.  Arbitrary boundary resolved with Embedded Boundary method.  2-D Transient Compressible Navier-Stokes Equations.  Second order Godunov method, for capturing strong shocks.  Diffusive terms (conductivity, viscosity) can depend on local state variables.  Adaptive Mesh Refinement employed to secure the uniform accuracy throughout the fluid domain.  Arbitrary boundary resolved with Embedded Boundary method. We Have Developed SPARTAN Chamber Dynamics and Clearing Code

3. Simulations to date (presented in past HAPL Meetings) have demonstrated:  Impact of diffusive terms: Important!  Impact of geometry: Important!  Impact of penetrations: Important!  Impact of background ionized gas (radiation, thermal conductivity): Important! Simulations to date (presented in past HAPL Meetings) have demonstrated:  Impact of diffusive terms: Important!  Impact of geometry: Important!  Impact of penetrations: Important!  Impact of background ionized gas (radiation, thermal conductivity): Important! SPARTAN Has Been Used to Explore Importance of Various Physical Phenomena Contours of Pressure, temperature, and density

4. During the Last Period We Focused on Improving the Numerics and Preparing for Production Runs  A new algorithm: Diffusive terms are now included as “source” terms and a new time-splitting method is used: Code is formally second-order everywhere. The new algorithm is essential in handling source/sink terms such as radiation energy loss, tracking target material that may be desorbed from the wall, etc.  Detailed convergence analysis has been performed and has confirmed the code accuracy and convergence.  We resolved the issue of “asymmetries” in the simulations.  SPARTAN was run successfully on a 16-node parallel processor with minimal changes in the code.  Each SPARTAN runs generates 100’s of MB of data. This is expected to grow substantially. We have started developing routine for data analysis.  A new algorithm: Diffusive terms are now included as “source” terms and a new time-splitting method is used: Code is formally second-order everywhere. The new algorithm is essential in handling source/sink terms such as radiation energy loss, tracking target material that may be desorbed from the wall, etc.  Detailed convergence analysis has been performed and has confirmed the code accuracy and convergence.  We resolved the issue of “asymmetries” in the simulations.  SPARTAN was run successfully on a 16-node parallel processor with minimal changes in the code.  Each SPARTAN runs generates 100’s of MB of data. This is expected to grow substantially. We have started developing routine for data analysis.

5.  Previous simulations (i.e., last HAPL Meeting), showed asymmetries in SPARTAN results for a symmetric problem. The asymmetries were typically less than 1-2% (expected code accuracy).  This was attributed to unstable nature of the flow.  Denis Colombant pointed out that instabilities growth are not sufficient to lead to this level of asymmetries.  Previous simulations (i.e., last HAPL Meeting), showed asymmetries in SPARTAN results for a symmetric problem. The asymmetries were typically less than 1-2% (expected code accuracy).  This was attributed to unstable nature of the flow.  Denis Colombant pointed out that instabilities growth are not sufficient to lead to this level of asymmetries. Previous SPARTAN Runs Developed Asymmetries Previous SPARTAN simulation showing up-down asymmetry T=100ms Pressure Contours T=100ms Density Contours

6.  The axis of symmetry was not located on a grid line. (It was chosen such that it was passing through the center of finest cell!)  Solution: Locate the center of chamber on the corner of one of the coarsest grids. It will always stay on the grid for even the finest grid.  The axis of symmetry was not located on a grid line. (It was chosen such that it was passing through the center of finest cell!)  Solution: Locate the center of chamber on the corner of one of the coarsest grids. It will always stay on the grid for even the finest grid. Resolution: Problem was not defined symmetrical! Computational Grid Physical Domain

7. SPARTAN Solution Is Now Symmetric With an Accuracy of < 10 -7 ! Previous Simulations: New Grid Positioning technique: t = 100 ms Density ContoursPressure Contours

8. Up-down symmetry enforced SPARTAN Solution Is Independent of Orientation of the Computational Grid Reference Case: Density Contours Mirror Image Up-down symmetry enforced  Differences among four solutions are < 1% (less than expected accuracy of solution)

9. Recent SPARTAN Simulations  Simulations of target deflection (Discussed in Ron Petzoldt Presentation) Impact of radiation from the background plasma:  It took some time to get the Coronal equilibrium data for Xe from UW in the form useful for SPARTAN. (Data was finalized last week).  In the mean time, we perform simulation assuming only bremsstrahlung. After the first bounce off the wall, the shocks convergence in the central portion of the chamber raising the temperature substantially: Without radiation, temperature raises at ~15 eV. With bremsstrahlung, temperature raises only to 4 eV. The total energy of the system (average temperature), however, was only reduced by 20%.  Based on the coronal equilibrium data, total radiation at ~15 eV is 10 4 times larger than bremsstrahlung. Thus, peak temperature will be even lower but not by much (Radiation drops significantly near 1-2 eV). The impact on total energy of the system would be probably smaller.  Simulations of target deflection (Discussed in Ron Petzoldt Presentation) Impact of radiation from the background plasma:  It took some time to get the Coronal equilibrium data for Xe from UW in the form useful for SPARTAN. (Data was finalized last week).  In the mean time, we perform simulation assuming only bremsstrahlung. After the first bounce off the wall, the shocks convergence in the central portion of the chamber raising the temperature substantially: Without radiation, temperature raises at ~15 eV. With bremsstrahlung, temperature raises only to 4 eV. The total energy of the system (average temperature), however, was only reduced by 20%.  Based on the coronal equilibrium data, total radiation at ~15 eV is 10 4 times larger than bremsstrahlung. Thus, peak temperature will be even lower but not by much (Radiation drops significantly near 1-2 eV). The impact on total energy of the system would be probably smaller.

10. Plans for the Next Period  Document recent advanced in numerical algorithm.  Update numerical algorithm to handle large diffusive terms (i.e., large radiation). Production Runs:  Compare simulation results from 2D Cartesian and 2D cylindrical geometry to determine if 2D simulation is sufficient and/or we should move to 3D.  Survey of impact of different chamber constituents, initial pressure, etc.  Simulation to investigate the impact of chamber evolution on other systems such as final optics, target injection and placement, etc.  Document recent advanced in numerical algorithm.  Update numerical algorithm to handle large diffusive terms (i.e., large radiation). Production Runs:  Compare simulation results from 2D Cartesian and 2D cylindrical geometry to determine if 2D simulation is sufficient and/or we should move to 3D.  Survey of impact of different chamber constituents, initial pressure, etc.  Simulation to investigate the impact of chamber evolution on other systems such as final optics, target injection and placement, etc.