Accelerating Poisson solvers in front tracking method using parallel direct methods. (English) Zbl 1390.76196

Summary: Parallel direct computation is implemented in multiphase flow simulation of bubbles in a curved duct using a front tracking method to improve the computational cost. To solve the density Poisson equation, three methods including the SOR, FGMRES and PARDISO are tested using two strategies of full domain and masked bubble. The comparison of numerical simulations at the same conditions indicates that the PARDISO scheme under the masked bubble strategy considerably reduces the computational time and RAM usage, which enables simulations on very fine grid resolutions.


76F65 Direct numerical and large eddy simulation of turbulence
76Txx Multiphase and multicomponent flows
65Y05 Parallel numerical computation
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs


Full Text: DOI


[1] Yuen-Yick, K.; Jie, S., An efficient direct parallel spectral-element solver for separable elliptic problems, J Comput Phys, 225, 1721-1735, (2007) · Zbl 1123.65116
[2] Borrell, R.; Lehmkuhl, O.; Trias, F. X.; Oliva, A., Parallel direct Poisson solver for discretisations with one Fourier diagonalisable direction, J Comput Phys, 230, 4723-4741, (2011) · Zbl 1416.76204
[3] Kuo-Long, P.; Guan-Chen, Y., Parallel strategies of front-tracking method for simulation of multiphase flows, Comput Fluids, 67, 123-129, (2012) · Zbl 1365.76236
[4] Thies J, Wubs F. Design of a parallel hybrid direct/iterative solver for CFD problems. In: Seventh IEEE international conference on eScience; 2011. · Zbl 1427.65038
[5] Schenk O, Gartner K. Sparse factorization with two-level scheduling in PARDISO. In: Proceedings of the 10th SIAM conference on parallel processing for scientific computing. Portsmouth, Virginia; 2001.
[6] Unverdi, S. O.; Tryggvason, G., A front-tracking method for viscous incompressible multi-fluid flows, J Comput Phys, 100, 25-37, (1992) · Zbl 0758.76047
[7] Schenk, O.; Gärtner, K., Solving unsymmetric sparse systems of linear equations with PARDISO, Future Gener Comput Syst, 20, 475-487, (2004)
[8] Schenk, O.; Gärtner, K., Two-level dynamic scheduling in PARDISO improved scalability on shared memory multiprocessing systems, Parallel Comput, 28, 187-197, (2002) · Zbl 0982.68195
[9] DeVries, B.; Iannelli, J.; Trefftz, C.; O’Hearn, Kurt A.; Wolffe, G., Parallel implementations of FGMRES for solving large, sparse non-symmetric linear systems, Proc Comput Sci, 18, 491-500, (2013)
[10] DeCecchis, D.; Ĺopez, H.; Molina, B., FGMRES preconditioning by symmetric/skew-symmetric decomposition of generalized Stokes problems, Math Comput Simul, 79, 1862-1877, (2009) · Zbl 1161.76033
[11] Peskin, C. S., Numerical analysis of blood flow in the heart, J Comput Phys, 25, 220, (1977) · Zbl 0403.76100
[12] Hoffman, K. A.; Chiang, S. T., Computational fluid dynamic, vol. 2, (2000), EES Wichita
[13] Nobari, M. R.; Jan, Y.-J.; Tryggvason, G., Phys Fluids, 8, 29-42, (1996)
[14] Tryggvason, G.; Bunner, B.; Esmaeeli, A., A front-tracking method for the computations of multiphase flow, J Comput Phys, 169, 708-759, (2001) · Zbl 1047.76574
[15] DeVries, B.; Iannelli, J.; Trefftz, C.; O’Hearn, Kurt A.; Wolffe, G., Parallel implementations of FGMRES for solving large, sparse non-symmetric linear system, Proc Comput Sci, 18, 491-500, (2013)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.