The Experts below are selected from a list of 73182 Experts worldwide ranked by ideXlab platform
Siddhartha Gupta - One of the best experts on this subject based on the ideXlab platform.
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a numerical approach to the non Uniqueness Problem of cosmic ray two fluid equations at shocks
Monthly Notices of the Royal Astronomical Society, 2021Co-Authors: Siddhartha Gupta, Prateek Sharma, A MignoneAbstract:Cosmic rays (CRs) are frequently modeled 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 modeling, and future directions are discussed.
A Mignone - One of the best experts on this subject based on the ideXlab platform.
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a numerical approach to the non Uniqueness Problem of cosmic ray two fluid equations at shocks
Monthly Notices of the Royal Astronomical Society, 2021Co-Authors: Siddhartha Gupta, Prateek Sharma, A MignoneAbstract:Cosmic rays (CRs) are frequently modeled 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 modeling, and future directions are discussed.
Si Duc Quang - One of the best experts on this subject based on the ideXlab platform.
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second main theorem and Uniqueness Problem of meromorphic mappings with moving hypersurfaces
arXiv: Complex Variables, 2013Co-Authors: Si Duc QuangAbstract:In this article, we establish some new second main theorems for meromorphic mappings of C m into P n (C) and moving hypersurfaces with truncated counting functions. A Uniqueness theorem for these mappings sharing few moving hypersurfaces without counting multiplicity is also given. This result is an improvement of the recent result of Dethlo - Tan [3]. Moreover the meromorphic mappings in our result may be algebraically degenerate. The last purpose of this article is to study Uniqueness Problem in the case where the meromorphic mappings agree on small identical sets.
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Uniqueness Problem with truncated multiplicities of meromorphic mappings in several complex variables
International Journal of Mathematics, 2006Co-Authors: Do Duc Thai, Si Duc QuangAbstract:In this article, the Uniqueness Problem with truncated multiplicities of meromorphic mappings in several complex variables is studied. The recent results of Smiley, Ji, Fujimoto and Fujimoto's questions are deduced as consequences.
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Uniqueness Problem with truncated multiplicities of meromorphic mappings in several complex variables for moving targets
International Journal of Mathematics, 2005Co-Authors: Do Duc Thai, Si Duc QuangAbstract:In this article, truncated second main theorems with moving targets are given. Basing on these theorems, the Uniqueness Problem with truncated multiplicities of meromorphic mappings in several complex variables for moving targets is solved.
Chunxia Meng - One of the best experts on this subject based on the ideXlab platform.
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the frequency averaged normal derivative integral equation to predict frequency averaged quadratic pressure radiated from structures
Engineering Analysis With Boundary Elements, 2017Co-Authors: Honglin Gao, Chunxia MengAbstract:Abstract Frequency averaged normal-derivative Helmholtz integral equation is proposed to get robust predictions of the frequency averaged quadratic pressure (FAQP) radiated from the structures at medium and high frequencies. The non-Uniqueness Problem of frequency averaged Helmholtz integral equation and frequency averaged normal-derivative Helmholtz integral equation is overcome by the coupling method combining these two integral equations. The numerical examples are given to demonstrate the versatility of the frequency averaged normal-derivative Helmholtz integral equation and the coupling method.
Prateek Sharma - One of the best experts on this subject based on the ideXlab platform.
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a numerical approach to the non Uniqueness Problem of cosmic ray two fluid equations at shocks
Monthly Notices of the Royal Astronomical Society, 2021Co-Authors: Siddhartha Gupta, Prateek Sharma, A MignoneAbstract:Cosmic rays (CRs) are frequently modeled 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 modeling, and future directions are discussed.
