Despite decades of development, Lagrangian hydrodynamics of strengthfree materials presents numerous open issues, even in one dimension. We focus on theproblem of closing a system of equations for a two-material cell ...Despite decades of development, Lagrangian hydrodynamics of strengthfree materials presents numerous open issues, even in one dimension. We focus on theproblem of closing a system of equations for a two-material cell under the assumptionof a single velocity model. There are several existing models and approaches, eachpossessing different levels of fidelity to the underlying physics and each exhibitingunique features in the computed solutions. We consider the case in which the changein heat in the constituent materials in the mixed cell is assumed equal. An instantaneous pressure equilibration model for a mixed cell can be cast as four equations infour unknowns, comprised of the updated values of the specific internal energy andthe specific volume for each of the two materials in the mixed cell. The unique contribution of our approach is a physics-inspired, geometry-based model in which theupdated values of the sub-cell, relaxing-toward-equilibrium constituent pressures arerelated to a local Riemann problem through an optimization principle. This approachcouples the modeling problem of assigning sub-cell pressures to the physics associated with the local, dynamic evolution. We package our approach in the frameworkof a standard predictor-corrector time integration scheme. We evaluate our model using idealized, two material problems using either ideal-gas or stiffened-gas equationsof state and compare these results to those computed with the method of Tipton andwith corresponding pure-material calculations.展开更多
This paper presents a study of pressure and velocity relaxation in twophase flow calculations.Several of the present observations have been made elsewhere,and the purpose of the paper is to strengthen these observatio...This paper presents a study of pressure and velocity relaxation in twophase flow calculations.Several of the present observations have been made elsewhere,and the purpose of the paper is to strengthen these observations and draw some conclusions.It is numerically demonstrated how a single-pressure two-fluid model is recovered when applying instantaneous pressure relaxation to a twopressure two-fluid model.Further,instantaneous velocity relaxation yields a driftflux model.It is also shown that the pressure relaxation has the disadvantage of inducing a large amount of numerical smearing.The comparisons have been conducted by using analogous numerical schemes,and a multi-stage centred(MUSTA)scheme for non-conservative two-fluid models has been applied to and tested on the two-pressure two-fluid model.As for other,previously tested two-phase flow models,the MUSTA schemes have been found to be robust,accurate and nonoscillatory.However,compared to their Roe reference schemes,they consistently have a lower computational efficiency for problems involving mass transport.展开更多
基金This work was performed under the auspices of the United States Department of Energy by Los Alamos National Security,LLC,at Los Alamos National Laboratory under contract DE-AC52-06NA25396.
文摘Despite decades of development, Lagrangian hydrodynamics of strengthfree materials presents numerous open issues, even in one dimension. We focus on theproblem of closing a system of equations for a two-material cell under the assumptionof a single velocity model. There are several existing models and approaches, eachpossessing different levels of fidelity to the underlying physics and each exhibitingunique features in the computed solutions. We consider the case in which the changein heat in the constituent materials in the mixed cell is assumed equal. An instantaneous pressure equilibration model for a mixed cell can be cast as four equations infour unknowns, comprised of the updated values of the specific internal energy andthe specific volume for each of the two materials in the mixed cell. The unique contribution of our approach is a physics-inspired, geometry-based model in which theupdated values of the sub-cell, relaxing-toward-equilibrium constituent pressures arerelated to a local Riemann problem through an optimization principle. This approachcouples the modeling problem of assigning sub-cell pressures to the physics associated with the local, dynamic evolution. We package our approach in the frameworkof a standard predictor-corrector time integration scheme. We evaluate our model using idealized, two material problems using either ideal-gas or stiffened-gas equationsof state and compare these results to those computed with the method of Tipton andwith corresponding pure-material calculations.
基金financed by SINTEF Energy Research and the Research Council of Norway.
文摘This paper presents a study of pressure and velocity relaxation in twophase flow calculations.Several of the present observations have been made elsewhere,and the purpose of the paper is to strengthen these observations and draw some conclusions.It is numerically demonstrated how a single-pressure two-fluid model is recovered when applying instantaneous pressure relaxation to a twopressure two-fluid model.Further,instantaneous velocity relaxation yields a driftflux model.It is also shown that the pressure relaxation has the disadvantage of inducing a large amount of numerical smearing.The comparisons have been conducted by using analogous numerical schemes,and a multi-stage centred(MUSTA)scheme for non-conservative two-fluid models has been applied to and tested on the two-pressure two-fluid model.As for other,previously tested two-phase flow models,the MUSTA schemes have been found to be robust,accurate and nonoscillatory.However,compared to their Roe reference schemes,they consistently have a lower computational efficiency for problems involving mass transport.
