An Analytical Approach of Computational Complexity for the Method of Multifluid Modeling


  • A.K. Borah Department of Mathematics, R G Baruah College, Gauhati University , Guwahati-781025 , India
  • P. K. Singh



Bi-Conjugate Gradient Stabilized (Bi-CGSTAB, ILUT Function, Krylov Subspace Preconditioner SIMPLE Algorithm, Multifluid Flows


In this paper we deal the building blocks of the computer simulation of the multiphase flows. Whole simulation procedure can be viewed as two super procedures, the implementation of VOF method and the solution of Navier Stoke’s Equation, Moreover, a sequential code for a Navier Stoke’s solver has been studied.


Mayer, A and Lenhard, R (1998), Special Issue on Multiphase Flows and Chemical Transport, Advances in Water Resource, 21: 75-76.

Christopher, E (2005), Fundamentals of Multiphase Flows Cambridge University, Press U.K.

Melvile, W (1996), The Role of Surface Wave Breaking in Air-Sea Interaction, Annual Review of Fluid Mechanics, 28: 279-321.

Rider, W and Kothe, D (1998), Reconstructing Volume Tracking , Journal of Computational Physics, 141: 112-152.

Greaves, D. (2004), A Quadrative Adaptive method for Simulating Fluid flow with moving Interfaces, Journal of Computational Physics, 194: 35-56.

Rudman, M (1997), Volume Tracking Methods for Interfacial Flow Calculations, International Journal of Numerical methods in Fluids, 24: 671-691.

Denis, G ., Ali, N., Scardovelli, R., and Zaleski, S. (1999), Volume-of-fluid interface tracking with Smoothed Surface Stress Methods for Three Dimensional Flows, Journal of Computational Physics, 152: 423-456.

Alibadi, S and Shujaee, K (2001). Free surface flow simulations using parallel finite element method, SIMULATION, 76(5): 257-262.

Scardovelli, R and Zaleski, S (2000), Analytical relations connecting Linear Interfaces and Volume Fractions in Rectangular Grids, Journal of Computational Physics, 164(6): 228-237.

Ruben, S and Zaleski, S (2003), Interface Reconstruction with Least-Square Fit and Split Eulerian Lagragian Advection, International Journal for Numerical Methods in Fluids, 41: 251-274.

Scardovelli, R and Zaleski, S (2003), Interface Reconstruction with Least Square fit and split Eulerian –Lagragian advection. International Journal of Numerical Methods in Fluids, 41: 251-274.

Saad, Y (1992), Preconditioning Techniques for Nonsymmetric Indefinite Linear systems. Technical Report, Centre for Supercomputing Research and Development, University of Illinois at Urbana Champaign.

Sun, J, Cao, J and Yang, C (2009). Paralled Preconconditioners for large scale partial differential equations systems, Journal of Computational and Applied mathematics, 226: 125-135.

Saad, Y (1996), Iterative methods for Sparse Linear System. PWS Publishing Company, International Thompson Publishing Inc. Bostan.

Basermann, A (2000), Parallel Block ILUT/ILDT Preconditioning for Sparse Eigen Problems and Sparse Linear system. Numerical Linear Algebra with Applications 7: 635-648.

Li, K (2005), First and Scalable Parallel Matrix Computations on Distributed memory Systems. In 19th IEEE International Parallel and Distributed Processing Symposium.

Shahnaz, R., Usman, A., and Chugati, I (2006), Implementation and Evaluation of parallel sparse Matrix-Vector products on Distributed Memory Parallel Computers, Barcelona, Spain. In IEEE International Conference on Cluster Computing (CLUSTER), Barcelona, Spain pages 1-6.

Straubhaar, J (2008), Parallel Preconditioners for the conjugate Gradient Algorithm using Gram Scimidt and least square methods, Parallel Computing, 34(10):551-569.




How to Cite

Borah, A., & Singh, P. K. (2015). An Analytical Approach of Computational Complexity for the Method of Multifluid Modeling. Transactions on Engineering and Computing Sciences, 2(6), 91.