8. Bibliography

1

Patrick K Notz, Roger P Pawlowski, and James C Sutherland. Graph-based software design for managing complexity and enabling concurrency in multiphysics pde software. ACM Transactions on Mathematical Software (TOMS), 39(1):1–21, 2012.

2

Michael L. Hobbs, Judith A. Brown, Michael J. Kaneshige, and Cuauhtemoc Aviles-Ramos. Cookoff of powdered and pressed explosives using a micromechanics pressurization model. Propellants, Explosives, Pyrotechnics, 47(2):e202100156, 2022. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/prep.202100156, arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/prep.202100156, doi:https://doi.org/10.1002/prep.202100156.

3

W. M. Deen. Analysis of Transport Phenomena. Topics in Chemical Engineering. Oxford University Press, New York, 1998.

4

Lawrence E. Malvern. Introduction to the Mechanics of a Continuous Medium. Series in Engineering of the Physical Sciences. Prentice-Hall, Upper Saddle River, NJ, USA, 1969.

5

George E. Mase. Theory and Problems of Continuum Mechanics. Schaum's Outline Series. McGraw-Hill, New York, NY, USA, 1970.

6

Javier Bonet and Richard D. Wood. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press, 1997.

7

Ted Belytschko, Wing Kam Liu, and Brian Moran. Nonlinear Finite Elements for Continua and Structures. John Wiley and Sons, 2004.

8

M. J. Martinez. Mathematical and numerical formulation of nonisothermal multicomponent three-phase flow in porous media. Technical Report SAND95-1247, Sandia National Laboratories, Albuquerque, NM, USA, 1995. http://www.prod.sandia.gov/cgi-bin/techlib/access-control.pl/1995/951247.pdf.

9

M. J. Martinez, P. L. Hopkins, and J. N. Shadid. LDRD final report: physical simulation of nonisothermal multiphase multicomponent flow in porous media. Technical Report SAND97-1766, Sandia National Laboratories, Albuquerque, NM, USA, 1997. http://www.prod.sandia.gov/cgi-bin/techlib/access-control.pl/1997/971766.pdf.

10

M. J. Martinez, P. L. Hopkins, and P. N. Reeves. PorSalsa user's manual. Technical Report SAND2001-1555, Sandia National Laboratories, Albuquerque, NM, USA, 2001. http://www.prod.sandia.gov/cgi-bin/techlib/access-control.pl/2001/011555.pdf.

11

Chris Lautenberger and Carlos Fernandez-Pello. Generalized pyrolysis model for combustible solids. Fire Safety Journal, 44(6):819–839, 2009.

12

D. K. Gartling, C. E. Hickox, and R. C. Givler. Simulations of coupled viscous and porous flow problems. Comp. Fluid Dyn., 1-2:23–48, 1997.

13

S. A. Roberts, D. R. Noble, E. M. Benner, and P. R. Schunk. Multiphase hydrodynamic lubrication flow using a three-dimensional shell finite element model. Comput. Fluids, 2013. , in press.

14

Ely M Gelbard. Application of spherical harmonics method to reactor problems. Bettis Atomic Power Laboratory, West Mifflin, PA, Technical Report No. WAPD-BT-20, 1960.

15

A. D. Kraus and A. Bar-Cohen. Thermal Analysis and Control of Electronic Equipment. Hemisphere, Washington DC, 1983.

16

J. H. Lienhard IV and J. H. Lienhard V. A Heat Transfer Textbook. Phlogiston Press, Cambridge, Massachusetts, 3rd edition, 2004. URL: http://web.mit.edu/lienhard/www/ahtt.html.

17

C. V. Madhusudana. Thermal Contact Conductance. Springer-Verlag, New York, 1996.

18

R. Siegel and J. R. Howell. Thermal Radiation Heat Transfer. Taylor and Francis, Washington, D.C., 1992.

19

M. W. Glass. Chaparral: a library for solving enclosure radiation heat transfer problems. Technical Report SAND01-xxxx, Sandia National Laboratories, Albuquerque, New Mexico, 2001.

20

B. R. Carnes and K. D. Copps. Thermal contact algorithms in sierra mechanics. Technical Report SAND2008-2607, Sandia National Laboratories, Albuquerque, New Mexico, April 2008.

21

D.N. Arnold, B. Cockburn, and L. D. Marini. Unified analysis of discontinuous galerkin methods for elliptic problems. SIAM J. Numer. Anal., 39:1749–79, 2002.

22

E. B. Becker, G. F. Carey, and J. T. Oden. Finite Elements: An Introduction. Prentice-Hall Inc., New Jersey, 1981.

23

T. R. Young. Chemeq—a subroutine for solving stiff ordinary differential equations. Technical Report NRL Memorandum Report 4091, Naval Research Laboratory, Washington D.C., 1980.

24

B. A. Finlayson. The Method of Weighted Residuals and Variational Principles. Academic Press, New York, 1972.

25

P. Gresho, R. Lee, R. Sani, and T. Stullich. On the time-dependent FEM solution of the incompressible navier-stokes equations in two and three dimensions. Recent Advances in Numerical Methods in Fluids, 1980.

26

D. K. Gartling, R. E. Hogan, and M. W. Glass. Coyote—a finite element computer program for nonlinear heat conduction problems, part I—theoretical background, version 4.05. Technical Report SAND94-1173, Sandia National Laboratories, Albuquerque, New Mexico, 2000.

27

D. K. Gartling, R. E. Hogan, and M. W. Glass. Coyote—a finite element computer program for nonlinear heat conduction problems, part II—user's manual, version 4.05. Technical Report SAND94-1179, Sandia National Laboratories, Albuquerque, New Mexico, 2000.

28

J. E. Marsden and A. J. Tromba. Vector Calculus. W. H. Freeman and Company, New York, 1981.

29

S. Domino. Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach. J. Comp. Phys, 359:331–351, 2018.

30

S. Domino, P. Sakievich, and M. Barone. A assessment of atypical mesh topologies for low-Mach large-eddy simulation. Comp. Fluids, 179:655–669, 2019.

31

Robert Moser, editor. Numerical Methods in Turbulence Simulation. Computation and Analysis of Turbulent Flows. Academic Press, San Diego, CA, December 2022.

32

G. S. Beavers and D. D. Joseph. Boundary conditions at a naturally permeable wall. J. Fluid Mech., 30:197–207, 1967.

33

P. G. Saffman. On the boundary condition at the surface of a porous medium. Studies in Applied Mathematics, 50(2):93–101, 1971.

34

R. H. Davis and H. A. Stone. Flow through beds of porous particles. Chemical Engineering Science, 48(23):3993–4005, 1993.

35

James A Sethian. A fast marching level set method for monotonically advancing fronts. Proceedings of the National Academy of Sciences, 93(4):1591–1595, 1996.

36

David R Noble, Elijah P Newren, and Jeremy B Lechman. A conformal decomposition finite element method for modeling stationary fluid interface problems. International Journal for Numerical Methods in Fluids, 63(6):725–742, 2010.

37

Bruno Lafaurie, Carlo Nardone, Ruben Scardovelli, Stéphane Zaleski, and Gianluigi Zanetti. Modelling merging and fragmentation in multiphase flows with surfer. Journal of computational physics, 113(1):134–147, 1994.

38

Richard A Cairncross, P Randall Schunk, Thomas A Baer, Rekha R Rao, and Phillip A Sackinger. A finite element method for free surface flows of incompressible fluids in three dimensions. part i. boundary fitted mesh motion. International journal for numerical methods in fluids, 33(3):375–403, 2000.

39

S Hysing. A new implicit surface tension implementation for interfacial flows. International Journal for Numerical Methods in Fluids, 51(6):659–672, 2006.

40

D. Dobranich. Safsim input manual -a compute program for the engineering simulation of flow systems. Technical Report SAND92-0694, Sandia National Laboratories, Albuquerque, NM, USA, September 1992.

41

Eric C Cyr, John N Shadid, and Raymond S Tuminaro. Teko: a block preconditioning capability with concrete example applications in navier–stokes and mhd. SIAM Journal on Scientific Computing, 38(5):S307–S331, 2016.

42

Eric C Cyr, John N Shadid, and Raymond S Tuminaro. Stabilization and scalable block preconditioning for the navier–stokes equations. Journal of Computational Physics, 231(2):345–363, 2012.

43

Youcef Saad. A flexible inner-outer preconditioned gmres algorithm. SIAM Journal on Scientific Computing, 14(2):461–469, 1993.

44

Robert Kosik, Peter Fleischmann, Bernhard Haindl, Paola Pietra, and Siegfried Selberherr. On the interplay between meshing and discretization in three-dimensional diffusion simulation. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 19(11):1233–1240, 2000.

45

Changna Lu, Weizhang Huang, and Jianxian Qiu. Maximum principle in linear finite element approximations of anisotropic diffusion–convection–reaction problems. Numerische Mathematik, 127(3):515–537, 2014.

46

Dmitri Kuzmin. Linearity-preserving flux correction and convergence acceleration for constrained galerkin schemes. Journal of Computational and Applied Mathematics, 236(9):2317–2337, 2012.

47

Dmitri Kuzmina and John N Shadidb. A new approach to enforcing discrete maximum principles in continuous galerkin methods for convection-dominated transport equations. Preprint: Ergebnisberichte des Instituts für Angewandte Mathematik, 2015.

48

I. M. Levi. Users' Guide to the Transient Heat Conduction Finite Element Code HTCON. Technical Report MM70-5425-17, Bell Telephone Laboratories, Whippany, NJ, USA, 1970.

49

A. F. Emery, K. Sugihara, and A. T. Jones. A comparison of some of the thermal characteristics of finite-element and finite-difference calculations of transient problems. Num. Heat Trans., 2:97–113, 1979.

50

F. Damjanic and D. R. J. Owen. Practical considerations for thermal transient finite element analysis using isoparametric elements. Nucl. Engrg. Des., 69:109–126, 1982.

51

E. Rank, C. Katz, and H. Werner. On the importance of the discrete maximum principle in transient analysis using finite element methods. Int. J. Num. Meth. Engng., 19:1771–1782, 1983.

52

H. S. Carslaw and J. C. Jaeger. Conduction of Heat in Solids. Clarendon Press, Oxford, 2\textsuperscript nd edition, 1959.

53

I. M. Krieger. Rheology of monodisperse latices. Adv. Colloid Interface Sci., 3:111–136, 1972.

54

D. K. Gartling. NACHOS II - a finite element computer program for incompressible flow problems. part I - theoretical background. Technical Report SAND86-1816, Sandia National Labs, Albuquerque, NM, USA, April 1986.

55

E. R. G. Eckert. Survey of boundary layer heat transfer at high velocities and high temperatures. Technical Report, WADC, 1960.

56

Clark R. Dohrmann and Pavel B. Bochev. A stabilized finite element method for the Stokes problem based on polynomial pressure projections. Int. J. Num. Meth. Fluids, 46:183–201, 2004.

57

Pavel B. Bochev, Clark R. Rohrmann, and Max D. Gunzburger. Stabilization of low-order mixed finite elements for the Stokes equations. SIAM J. Numer. Anal., 44(1):82–101, 2006.

58

T. Hughes, L. P. Franca, and M. Balestra. A new finite element formulation for computational fluid dynamics: v. circumventing the babuska-brezzi condition: a stable petrov-galerkin formulation of the stokes problem accomodating equal-order interpolations. Comput. Methods Appl. Mech. Engrg., 59:85–99, 1986.

59

S. Gordan and B. J. McBride. Computer program for calculation of complex chemical equilibrium compositions and applications I. analysis. Technical Report Ref. Publication 1311, NASA, October 1994.

60

B. J. McBride and S. Gordan. Computer program for calculation of complex chemical equilibrium compositions and applications II. users manual and program description. Technical Report Ref. Publication 1311, NASA, June 1996.