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Oliveira, Anabela; Baptista, António M.
doi: 10.1002/fld.1650210302pmid: N/A
Selected finite element Eulerian‐Lagrangian methods for the solution of the transport equation are compared systematically in the relatively simple context of 1D, constant coefficient, conservative problems. A combination of formal analysis and numerical experimentation is used to characterize the stability and accuracy that results from alternative treatments of the concentrations at the feet of the characteristic lines. Within the methods analyzed, those that approach such treatment with the perspective of ‘integration’ rather than ‘interpolation’ tend to have superior accuracy. Exact integration leads to unconditional stability and excellent accuracy. Quadrature integration leads only to conditional stability, but newly derived criteria show that stability restrictions are relatively mild and should not preclude the usefulness of quadrature integration methods in a range of practical applications. While conclusions cannot be extended directly to multiple dimensions and complex flows and geometries, results should provide useful insight to the development and behaviour of specific Eulerian‐Lagrangian transport models.
doi: 10.1002/fld.1650210303pmid: N/A
The Van Leer method for the computation of convective fluxes is extended to two‐phase flow. By preventing spurious undershoots and overshoots, the scheme preserves physical realism while maintaining high‐order accuracy. This is particulary important for two‐phase flows, since phase exchange terms are typically a function of volume fraction products and numerical diffusion can incorrectly mix the two phases. The scheme described here is constructed to guarantee that the sum of the volume fractions is always unity and that the volume fractions are always greater than or equal to zero. Various test problems are computed to demonstrate the accuracy of the method and to show how the scheme might be incorporated in existing computational methods. In addition to multiphase flow applications, setting equal phase velocities results in a volume marker scheme that is well suited to single‐phase interface tracking problems.
doi: 10.1002/fld.1650210304pmid: N/A
This paper scrutinizes the predictive ability of the differential stress equation model in complex shear flows. Two backward‐facing step flows with different expansion ratios are solved by the LRR turbulence model with an anisotropic dissipation model and the near‐wall regions of the separated side resolved by a near‐wall model. The computer code developed for solving the transport equations is based on the finite‐volume‐finite‐difference method. In the numerical solution of the time‐averaged momenum equations the Reynolds stresses are treated partially as a diffusion term and partially as a source term to avoid numerical instability. Computational results are compared with experimental data. It is found that the near‐wall region of the separated side resolved by the near‐wall model, the LRR model with a simple modification of an anisotropic dissipation model can predict backward step flows well.
Ströll, H.; Durst, F.; Perić, M.; Scheuerer, G.
doi: 10.1002/fld.1650210305pmid: N/A
This paper presents results of the numerical study of a piston‐driven unsteady flow in a pipe with sudden expansion. The piston closes the larger‐diameter pipe and moves between two limiting positions with strong acceleration or deceleration at the beginning and end of each stroke and constant velocity in between. The piston velocity in the exhaust stroke is about four times higher than in the intake stroke. Periodic piston movement in this fashion creates a complex unsteady flow between the piston head and the plane of sudden expansion. The numerical method is implicit and of finite volume type, using a moving grid and a collocated arrangement of variables. Second‐order spatial discretization, fine grids and a multigrid solution method were used to ensure high accuracy and good efficiency. Spatial and temporal discretization errors were of the order of 1% and 0.1% respectively. The features of the flow are discussed and the velocity profiles are compared with experimental data, showing good qualitative and quantitative agreement.
doi: 10.1002/fld.1650210306pmid: N/A
A one‐dimensional, time‐dependent, isothermal, homogeneous, two‐phase flow model was developed to study magma ascent in volcanic conduits. The physical modeling equations were numerically solved by means of a TVD (total variation diminishing) predictor‐corrector procedure and by means of a predictor‐corrector technique based on the method of characteristics. The results from the transient model were verified with an analytical solution for wave propagation in conduits without friction and gravitational effects. The numerical solutions were also compared with those of a steady‐state, homogeneous, two‐phase model for basaltic and rhyolitic magma ascents in the fissures and circular conduits of Vesuvius and Mt St. Helens. An application of the model to magma decompression in conduits indicates very short times for gas exsolution, fragmentation, and shock wave propagation, implying that the modelling of gas exsolution should involve non‐equilibrium kinetics effects. Future coupling of the transient magma ascent model with magma chamber and pyroclastic dispersion models should allow for more realistic simulations of the time‐dependent behavior of real volcanic eruptions.
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