Fire Dynamics Simulator: Advances on simulation capability for - PowerPoint PPT Presentation

Fire Dynamics Simulator: Advances on simulation capability for complex geometry ed tape – such as the CityCent Marcos Vanella a,b , Randall McDermott b , Glenn Forney b , Kevin McGrattan b a The George Washington University b National Institute of Standards and Technology Thunderhead Engineering Fire and Evacuation Modelling Technical Conference 2016. Torremolinos, Spain. November 16 th -18 th , 2016.

Contents  Motivation and Objective.  Defining cut-cells: Computational geometry.  Scalar transport near internal boundaries. ed tape – such as the CityCent  The energy equation, thermodynamic divergence constraint.  Reconstruction for momentum equations. Divergence equivalence.  Poisson equation.  Examples.  Future work.

Motivation, Objective The Fire Dynamics Simulator* (FDS) is used in: • performance-based design of fire protection systems, • forensic work, • Simulation of wild land fire scenarios. Uses block-wise structured, rectilinear grids for gas phase, and “ lego- block” geometries to represent internal boundaries. Objective : ed tape – such as the CityCent • Develop an efficient, conservative numerical scheme for Fire-Structure Interaction: 12 MW fire load on a treatment of complex geometry within FDS. steel/concrete floor connection assembly. Velocity vectors (35 m/s [78 mph] max [red]) LES of 800 KW propane fire in open train cart. Geometry courtesy of Fabian for a wind field in Mill Creek Canyon, Utah. Braennstroem (Bombardier). 4 km x 4 km horizontal domain, 1 km vertical. 40 m grid resolution on a single mesh. * K. McGrattan et al. Fire Dynamics Simulator, Tech. Ref. Guide, NIST. Sixth Ed., Sept. (2013).

Motivation, Objective Unstructured Spatial discretization and time marching in FDS, work areas: “cut - cell” Structured Scalar r n + 1 , Y a n + 1 transport - 1 é ù n a T n + 1 = pW n + 1 W n + 1 = å Small cell T n + 1 n + 1 ê ú Y a / W , EOS a r n + 1 R ë û a= 1 Facet ed tape – such as the CityCent Combustion, Radiation ( ) n + 1 Divergence Ñ× u Constraint* æ ö ¶ u IB = - ¶ u ( ) - Ñ H n - 1 ¶ t = - F + Ñ H n - 1 F ç ÷ è ¶ t ø n + 1 - Ñ× u n D ( ) ) @ Ñ× u é ù ¶ , D H = - Ñ× F + ¶ Momentum ( ( ) Ñ× u Ñ× u ê ú + IBM + ë û ¶ t D t ¶ t ¶ u = - ( F + Ñ H ) u n + 1 D H n ¶ t * R. J. McDermott. J. Comput. Phys. 274, pp. 413-431 (2014); + E. A. Fadlun et al. J. Comput. Phys. 161, pp. 35-60 (2000).

Computational Geometry Objective: Regular Cells • Define cut-cell volumes of Cartesian cells intersected by body. • Robust, general, parallelizable. GASPHASE • Ideally efficient for moving object problem. cut-cells Data Management: ed tape – such as the CityCent SOLID • Work by Eulerian mesh block. Body surfaces defined by triangulations. • Hierarchical data structures are defined, capable of arbitrary number of cut-faces and cut-cells per Cartesian counterparts. Smokeview Visualization inclined C-beam mid-plane. Obtained with computational - Cartesian Level i , j geometry engine in FDS. IBM_CUTCELL(m) ii - Cut-cell Level jj IBM_CUTCELL(m)%CCELEM(ii)

Computational Geometry Scheme: • Body-plane intersection elements (segments, triangles) are defined for all Cartesian grid planes. Intersections along surface triangles also defined. • Cut-faces on Cartesian planes are defined by ed tape – such as the CityCent joining segments. Same for cut-faces along triangles. • Working by Cartesian cell, cut face sets are found for each cut-cell volume. • Area and volume properties are computed for each cut-face and cell. • Interpolation stencils are found for centroids Cut-cell definition on original Matlab implementation. (IBM).

Scalar Transport Based on mass fractions: on domain + Ics, Bcs æ ö J a = - r D a Ñ Y a = - D a Ñ ( r Y a ) - D a r Ñ r ( r Y a ) ç ÷ Take: è ø Then: ed tape – such as the CityCent Finite Volume method: Divide the domain on cells. • Advection: nfc å ò ò ( ) ( ) × ˆ ( ) k × ˆ Ñ× u r Y a ¢ d W = u r Y a ¢ d ¶ W = u r Y a ¢ n ii n ii , k A k W ii ¶ W ii k = 1 For a given face ( k=4, cut-cell ii ): é ù æ ö lin D a fl u k + r Y a ( ) k × ˆ ( ) k ( ) k u r Y a ¢ n ii , k A k = r Y a r Ñ r ú× ˆ ê ç ÷ n ii , k A k è ø ë û k nfc å ò ò ( ) ( ) × ˆ ( ) k × ˆ • Ñ× D a Ñ ( r Y a ) d W = D a Ñ ( r Y a ) d ¶ W = D a Ñ ( r Y a ) n ii n ii , k A k Diffusion: W ii ¶ W ii k = 1

Scalar Transport a ) n - D n u n ( r Y ¢ a Ñ ( r Y a ) n - Small cut-cells are problematic for explicit time integration. - Alleviation methods tend to be arbitrary, deteriorating the EX solution quality. Explicit - Implicit time integration*: SOLID ˆ n • Explicit region : Advance first. IM • Implicit region : linearizing transport, i.e. implicit BE: ed tape – such as the CityCent EXIM boundary ( r Y a ) n + 1 - ( r Y a ) n ( u n ( r Y a ) n + 1 - D n ) ¢ a Ñ ( r Y a ) n + 1 = - Ñ× n + 1 - D ¢ n ( r Y a Ñ ( r Y n + 1 n u D t a ) a ) 10 −2 1 1 SSPRK2 + BE 10 −3 *- C.N. Dawson, T.F. Dupont. SSPRK2 |err q | inf 1 SIAM J. Numer. Analysis 10 −4 2 31:4, pp. 1045-1061 (1994). SSPRK2 + BE & - S. May, M. Berger. Proc. TR 10 −5 Finite Vol. Cmplx App. VII, pp. 393-400 (2014). 10 −6 0.01 0.025 0.05 D t

Scalar Transport ( r Y a ) n + 1 - Number cell centered unknowns for . 2 - Build face lists on implicit region (cut-face and 3 7 regular, GASPHASE or INBOUNDARY). 4 - Advection diffusion matrices are built by face. unk = 1 5 6 End result in CSR format. - The corresponding discretized matrix-vector ed tape – such as the CityCent system: Very 8 small cell Implicit (BE): n + 1 = M r Y n +D t f ( ) é ù { } { } { } M +D t A adv + A diff û r Y ë a a - Implicit: Solve using the Intel MKL Pardiso . Explicit: Trivial as M is diagonal. Vol CC < C link Vol Cart - Very small cells cause ill conditioned systems. Link small cells to neighbors when C link » 10 - 4 and . n + 1 = M - D n +D t f ( ) é ù [ ] r Y { } { } { } t A adv + A diff û r Y C link » 0.95 M - Fully explicit option (FE): ë a a

Energy We factor the velocity divergence from the sensible enthalpy evolution equation (FDS). Objective: • Discretize terms in thermodynamic divergence consistently with the scalar transport formulation for cut-cells (unstructured finite volume mesh). • Use divergence integral equivalence to relate this divergence to the FDS Cartesian mesh. Our Scheme: ed tape – such as the CityCent GASPHASE � regular� cells� • Implemented transport terms in cut-cells. • Added combustion in regular cells of cut-cell 5� GASPHASE region, radiation next. 6� • cut-cell� Linked cells for scalar transport get volume SOLID 4� averaged thermodynamic divergence. ii cut-cell� 1� 2� 3� Solid SOLID Forced jj regular� cell� Schematic of cut-cell in 2D: velocities and fluxes on faces, and scalars defined in cells.

Momentum Coupling Scheme sequence: 1. Time advancement of scalars on cut-cells and regular gas cells. 2. IBM Interpolation to get target velocities in cut-faces ibm = c 0 u i B + c 1 u i u i int Gas ed tape – such as the CityCent ii 1. Flux average target velocities to Cartesian faces. ibm = å 1 ibm A cf u i ( u i ) k A cart k Solid 1. Compute direct forcing at Cartesian level : ( ) ii th Ñ× u 1. Compute thermodynamic divergence on cut-cells.

Momentum Coupling 6. Use divergence integral equivalence ò å ò ( ) ( ) ii th th Ñ× u d W = Ñ× u d W ( ) ii th Ñ× u Gas W cart W ii ii ( ) ii th Ñ× u to get Cartesian level target divergence . 7. Solve Cartesian level Poisson equation ed tape – such as the CityCent th - Ñ× u æ ö Solid ( ) ( ) n Ñ 2 H = - Ñ× F n + Ñ× u ç ÷ ç ÷ D t è ø (in order to avoid mass penetration into body, solve on gas phase and cut-cell underlying Cartesian cells). u n + 1 = u n - D t F n + Ñ H ( ) 8. Project Cartesian velocities into target divergence field 9. Reconstruct cut-face velocities.

Poisson Equation • IBM: solve Poisson equation on the whole Cartesian domain, including cells within the immersed solids. • Introduces mass penetration into the solid on the projection step. Undesirable for conservation, combustion. • Our Momentum Coupling scheme: use this type of Pressure solver, or an unstructured solution on Cartesian gas cells and cells underlying cut cells . ed tape – such as the CityCent H Global linear system solver: • Building a global Laplacian matrix in parallel. • Building the global RHS. • Calling Parallel Matrix-Vector solver, currently MKL cluster sparse direct solver . • Capability to define correct H boundary Solid condition in FDS &OBSTS and complex geometry bodies &GEOM. ¶ H = 0 ¶ x n