scholarly journals Exact Expressions for the Critical Mach Numbers in the Two‐Fluid Model of Cosmic‐Ray–modified Shocks

2001 ◽  
Vol 546 (1) ◽  
pp. 429-446 ◽  
Author(s):  
Peter A. Becker ◽  
Demosthenes Kazanas
Keyword(s):  
Fluid Model ◽  
Cosmic Ray ◽  
Mach Numbers ◽  
Two Fluid Model ◽  
Two Fluid

scholarly journals Time-dependent simulation of oblique MHD cosmic-ray shocks using the two-fluid model

1995 ◽  
Vol 441 ◽  
pp. 629 ◽  
Author(s):  
Adam Frank ◽  
T. W. Jones ◽  
Dongsu Ryu
Keyword(s):  
Fluid Model ◽  
Cosmic Ray ◽  
Time Dependent ◽  
Two Fluid Model ◽  
Two Fluid

scholarly journals A numerical approach to the non-uniqueness problem of cosmic ray two-fluid equations at shocks

2021 ◽  
Vol 502 (2) ◽  
pp. 2733-2749
Author(s):  
Siddhartha Gupta ◽  
Prateek Sharma ◽  
Andrea Mignone
Keyword(s):  
Large Scale ◽  
Fluid Model ◽  
Cosmic Ray ◽  
Numerical Approach ◽  
Uniqueness Problem ◽  
Test Problems ◽  
Fluid Approximation ◽  
Fluid Equations ◽  
Two Fluid Model ◽  
Two Fluid

ABSTRACT Cosmic rays (CRs) are frequently modelled as an additional fluid in hydrodynamic (HD) and magnetohydrodynamic (MHD) simulations of astrophysical flows. The standard CR two-fluid model is described in terms of three conservation laws (expressing conservation of mass, momentum, and total energy) and one additional equation (for the CR pressure) that cannot be cast in a satisfactory conservative form. The presence of non-conservative terms with spatial derivatives in the model equations prevents a unique weak solution behind a shock. We investigate a number of methods for the numerical solution of the two-fluid equations and find that, in the presence of shock waves, the results generally depend on the numerical details (spatial reconstruction, time stepping, the CFL number, and the adopted discretization). All methods converge to a unique result if the energy partition between the thermal and non-thermal fluids at the shock is prescribed using a subgrid prescription. This highlights the non-uniqueness problem of the two-fluid equations at shocks. From our numerical investigations, we report a robust method for which the solutions are insensitive to the numerical details even in absence of a subgrid prescription, although we recommend a subgrid closure at shocks using results from kinetic theory. The subgrid closure is crucial for a reliable post-shock solution and also its impact on large-scale flows because the shock microphysics that determines CR acceleration is not accurately captured in a fluid approximation. Critical test problems, limitations of fluid modelling, and future directions are discussed.

scholarly journals Natural modes of the two-fluid model of two-phase flow

2021 ◽  
Vol 33 (3) ◽  
pp. 033324
Author(s):  
Alejandro Clausse ◽  
Martín López de Bertodano
Keyword(s):  
Two Phase Flow ◽  
Fluid Model ◽  
Phase Flow ◽  
Two Phase ◽  
Natural Modes ◽  
Two Fluid Model ◽  
Two Fluid

Self-consistent hydrodynamic two-fluid model of vortex plasma

2021 ◽  
Vol 33 (3) ◽  
pp. 037116
Author(s):  
Victor L. Mironov
Keyword(s):  
Fluid Model ◽  
Self Consistent ◽  
Two Fluid Model ◽  
Two Fluid

scholarly journals Mathematical study on two-fluid model for flow of K–L fluid in a stenosed artery with porous wall

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
R. Ponalagusamy ◽  
Ramakrishna Manchi
Keyword(s):  
Theoretical Study ◽  
Fluid Model ◽  
Porous Wall ◽  
Governing Equations ◽  
Rate Of Increase ◽  
Special Cases ◽  
Stenosed Artery ◽  
Flow Through ◽  
Two Fluid Model ◽  
Two Fluid

AbstractThe present communication presents a theoretical study of blood flow through a stenotic artery with a porous wall comprising Brinkman and Darcy layers. The governing equations describing the flow subjected to the boundary conditions have been solved analytically under the low Reynolds number and mild stenosis assumptions. Some special cases of the problem are also presented mathematically. The significant effects of the rheology of blood and porous wall of the artery on physiological flow quantities have been investigated. The results reveal that the wall shear stress at the stenotic throat increases dramatically for the thinner porous wall (i.e. smaller values of the Brinkman and Darcy regions) and the rate of increase is found to be 18.46% while it decreases for the thicker porous wall (i.e. higher values of the Brinkman and Darcy regions) and the rate of decrease is found to be 10.21%. Further, the streamline pattern in the stenotic region has been plotted and discussed.

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