Three-dimensional spectral element simulations of variable density and viscosity, miscible displacements in a capillary tube |
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Authors: | Dirk Wilhelm |
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Affiliation: | Department of Mechanical and Environmental Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA |
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Abstract: | A high-accuracy numerical approach is introduced for three-dimensional, time-dependent simulations of variable density and viscosity, miscible flows in a circular tube. Towards this end, the conservation equations are treated in cylindrical coordinates. The spatial discretization is based on a mixed spectral element/Fourier spectral scheme, with careful treatment of the singularity at the axis. For the temporal discretization, an efficient semi-implicit method is applied to the variable viscosity momentum equation. This approach results in a constant coefficient Helmholtz equation, which is solved by a fast diagonalization method. Numerical validation data are presented, and simulations are conducted for the three-dimensionally evolving instability resulting from an unstable density stratification in a vertical tube. Some preliminary comparisons with corresponding experiments are undertaken. |
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Keywords: | 47.11.+j 47.20.Ma |
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