Experiences Extending the CFD Solver of the
PDE Framework Peano
T. Neckel, M. Lieb, R. Sangl
TUM, Department of Informatics, Chair of Scientific Computing in Computer Science
P. Schoeffel, F. Weyermann
Gesellschaft für Anlagen- und Reaktorsicherheit (GRS)
T. Neckel et al. www5.in.tum.de
SIAM CS&E 2011, Reno, March 2011
Outline
• The PDE Framework Peano
• Thermohydraulic Simulations
– Goals & Approach– Numerical Experiments
• Outlook
source: T. Weinzierl
• Cartesian grids
(recursive adaptivity, full grid hierarchy) • Low memory requirements
• Space-Filling curves + stack data structures
high cache-hit rates (>98%)
flexible insertion/deletion of data (grid changes) • Shared/distributed mem. parallelisation
• Software engineering aspects • CFD component
– Incompressible flow (FEM, IDO)
– Explicit + implicit time-integration schemes (FE, RK4, BE, (adaptive) TR)
T. Neckel et al. www5.in.tum.de
SIAM CS&E 2011, Reno, March 2011
• ordering of cells along a Peano curve
• stacks as non-persistent data structure
• adaptivity & generating systems
multi-level
• cell-oriented operator evaluation
• no separation of grid points and DoF (1 package/data type)
• high spatial and time locality of data access
• well suited for grid changes (insertion/deletion)
4
Thermohydraulic Simulations – Goals & Approach
• Typical approach:
– 1D FVM for overall pipe setup – 3D compressible simulations
for special sections • Idea (Peano usage):
– incompressible flow for special sections
– couple overall pipe setup and 3D simulations
T. Neckel et al. www5.in.tum.de
SIAM CS&E 2011, Reno, March 2011
Thermohydraulic Simulations – Goals & Approach
• Incompressible Navier-Stokes Equations
• Discretisation
Thermohydraulic Simulations – Goals & Approach
• Incompressible Navier-Stokes Equations
• Discretisation
– low-order FEM (Q1Q0, etc.)
• Boussinesq approximation
– energy conservation: temperature T
– Buoyancy term in momentum equation
T. Neckel et al. www5.in.tum.de
SIAM CS&E 2011, Reno, March 2011
Validation of Thermal Heat Transfer
Validation of Thermal Heat Transfer II
2D flat plate in parallel flow
Pr = 7
T. Neckel et al. www5.in.tum.de
SIAM CS&E 2011, Reno, March 2011
Validation of Thermal Heat Transfer III
3D natural convection
T. Neckel et al. www5.in.tum.de
SIAM CS&E 2011, Reno, March 2011
T. Neckel et al. www5.in.tum.de
SIAM CS&E 2011, Reno, March 2011
Outlook
• Thorough analysis of Cold Leg
• Turbulent effects (LES or turbulence model) • Two-phase flow
T. Neckel et al. www5.in.tum.de
SIAM CS&E 2011, Reno, March 2011
The PDE Framework Peano
T. Neckel et al. www5.in.tum.de
SIAM CS&E 2011, Reno, March 2011
Div-free Elements – Driven Cavity
Div-free Elements – Flow around a Cylinder
# DoF Re = 20 Re = 100
cd cl cd,max cl,max St 88,857 5.68 0.0151 3.225 0.94 0.299 ref. 5.58 0.0107 3.230 1.00 0.298
T. Neckel et al. www5.in.tum.de
SIAM CS&E 2011, Reno, March 2011
CFD Extensions
• Moving geometries
– Update of data + grid (regular + adaptive) – Divergence correction
The PDE Framework Peano
• Cartesian grids (arbitrary dimensions) • Plug-in concept for applications
• Space-filling curves, spacetrees, and stack data structures – Strictly element-wise access
– Low memory demands – Dynamical load balancing
– Moving geometries, dynamical adaptivity, geometric multigrid • Software Engineering
– automatic tests, continuous integration, OO, design patterns, ... • CFD component
– Incompressible flow (FEM, IDO)
– Explicit + implicit time-integration schemes (FE, RK4, BE, (adaptive) TR)
T. Neckel et al. www5.in.tum.de
SIAM CS&E 2011, Reno, March 2011
Backup I
Low memory requirements (FEM + adap.):
0 500 1000 1500 2000 2500 FE RK TR adap. sundance bytes 2D bytes 3D
T. Neckel et al. www5.in.tum.de
SIAM CS&E 2011, Reno, March 2011
Numerical Results - Performance
2D IDO Overhead Peano vs. Aoki (regular):
1.3 – 4.4
0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 2 level 6 12,676 level 7 116,061 level 8 1,051,253
ratio adaptive vs. regular
