A novel partial differential algebraic equation (PDAE) solver: Iterative space-time conservation element/solution element (CE/SE) method

Computers and Chemical Engineering

Volumn 28, Issue 8, 2004, Pages 1309-1324

  Lim, Young Il ^a   Chang, Sin Chung ^b   Jørgensen, Sten Bay ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b NASA GLENN RESEARCH CENTER   (United States)

Author keywords

Chromatographic adsorption problem; Method of lines (MOL); Numerical analysis; Partial differential algebraic equations (PDAEs); Protein ion exchange separation; Space time CE SE method

Indexed keywords

ADSORPTION ISOTHERMS; ALGEBRA; ITERATIVE METHODS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS;

CONSERVATION ELEMENT (CE); SOLUTION ELEMENT (SE);

CHEMICAL ENGINEERING;

ALGORITHM; CHROMATOGRAPHY; COMPUTER; ION EXCHANGE; MATHEMATICAL ANALYSIS; MEMBRANE; MODEL;

ACCURACY; ARTICLE; CHROMATOGRAPHY; DIFFUSION; ISOTHERM; MATHEMATICAL COMPUTING; MATHEMATICAL PARAMETERS; NONLINEAR SYSTEM; SPACE; STATISTICAL SIGNIFICANCE; THERMODYNAMICS; TIME;

EID: 2342580778     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compchemeng.2003.09.016     Document Type: Article

References (28)

1. Beste Y.A., Lisso M., Wozny G., Arlt W. Optimization of simulated moving bed plants with low efficient stationary phases: Separation of fructose and glucose. Journal of Chromatography A. 868:2000;169-188
2. Bromley L.A. Thermodynamic properties of strong electrolytes in aqueous solutions. AIChE Journal. 19(2):1973;313-320
3. Brooks C.A., Cramer S.M. Steric mass-action ion exchange: Displacement profiles and induced salt gradients. AIChE Journal. 38(12):1992;1969-1978
4. Chang S.C. The method of space-time conservation element and solution element - A new approach for solving the Navier-Stokes and Euler equations. Journal of Computers and Physics. 119:1995;295-324
5. Chang, S. C. (2002). Courant number insensitive CE/SE schemes. In Proceedings of the 38th AIAA Joint Propulsion Conference. AIAA-2002-3890, Indianapolis, USA.
6. Chang, S. C., & To, W. M. (1991). A new numerical framework for solving conservation laws - The method of space-time conservation element and solution element. NASA TM 104495.
7. Chang S.C., Wang X.Y., Chow C.Y. The space-time conservation element and solution element method: A new high-resolution and genuinely multidimensional paradigm for solving conservation laws. Journal of Computers and Physics. 156:1999;89
8. Chang, S. C., Wang, X. Y., Chow, C. Y., & Himansu, A. (1995). The method of space-time conservation element and solution element - Development of a new implicit solver. NASA TM 106897.
9. Chang S.C., Wang X.Y., To W.M. Application of the space-time conservation element and solution element method to one-dimensional convection-diffusion problems. Journal of Computers and Physics. 165:2000;189-215
10. Chang, S. C., Wu, Y., Wang, X. Y., & Yang, V. (2000). Local mesh refinement in the space-time CE/SE method. In Proceeding of the First International Conference on CFD (pp. 61-66). Kyoto, Japan.
11. Dunnebier G., Weirich I., Klatt K.-U. Computationally efficient dynamic modeling and simulation of simulated moving bed chromatographic processes with linear isotherms. Chemical Engineering Science. 53(14):1998;2537-2546
12. Hindmarsch A.C. LSODE and LSODI: Two new initial value ordinary differential equation solvers. ACM SIGNUM Newsletter. 15:1980;19-21
13. Jiang G., Shu C.W. Efficient implementation of weighted ENO schemes. Journal of Computers and Physics. 126:1996;202-228
14. Li Y., Pinto N.G. Model for ion-exchange equilibria of macromolecules in preparative chromatography. Journal of Chromatography A. 702:1995;113-123
15. Lim Y.I., Le Lann J.M., Joulia X. Accuracy, temporal performance and stability comparisons of discretization methods for the solution of Partial Differential Equations (PDEs) in the presence of steep moving fronts. Computational Chemical Engineering. 25:2001a;1483-1492
16. Lim Y.I., Le Lann J.M., Joulia X. Moving mesh generation for tracking a shock or steep moving front. Computational Chemical Engineering. 25:2001b;653-663
17. Lim Y.I., Le Lann J.M., Meyer X.M., Joulia X., Lee G.B., Yoon E.S. On the solution of Population Balance Equations (PBE) with accurate front tracking methods in practical crystallization processes. Chemical Engineering Science. 57:2002;177-194
18. Ma Z., Wang N.-H.L. Standing wave analysis of SMB chromatography: Linear systems. AIChE Journal. 40(10):1997;2488-2508
19. Melis S., Markos J., Cao G., Morbidelli M. Separation between amino acids and inorganic ions through ion exchange: Development of a lumped model. Ind. Eng. Chem. Res. 35:1996;3629-3636
20. Molls T., Molls F. Space-time conservation method applied to Saint Venant equations. Journal of Hydraulic Engineering. 124(5):1998;501-508
21. Motz S., Mitrovic A., Gilles E.-D. Comparison of numerical methods for the simulation of dispersed phase systems. Chemical Engineering Science. 57:2002;4329-4344
22. Pennington, S. V., & Berzins, M. (1993). New NAG library software for first-other partial differential equations. Research report series 93.21, University of Leeds, Leeds.
23. Petzold, L. R. (1983). In R. S. Stepleman, et al. (Eds.), A description of DASSL: A differential/algebraic system solver in scientific computing (pp. 65-68). North-Holland, Amsterdam.
24. Poulain C.A., Finlayson B.A. A comparison of numerical methods applied to non-linear adsorption columns. International Journal of Numerical Methods and Fluids. 17(10):1993;839-859
25. Raje P., Pinto N.G. Combination of the steric mass action and non-ideal surface solution models for overload protein ion-exchange chromatography. Journal of Chromatography A. 760:1997;89-103
26. Talu O., Zwiebel I. Multicomponent adsorption equilibria of nonideal mixture. AIChE Journal. 32(8):1986;1263-1276
27. Yu, S. T., & Chang, S. C. (1997). Treatment of stiff source terms in conservation laws by the method of space-time CE/SE, AIAA 97-0435, In Proceedings of the 35th Aerospace Sciences Meeting. Reno, USA.
28. Zhang Z.C., Yu S.T., Chang S.C. A space-time conservation element and solution element method for solving the two- and three-dimensional unsteady Euler equations using quadrilateral and hexahedral meshes. Journal of Computers and Physics. 175:2002;168-199