Numerical Calculations of the GRP Scheme for Nonconservative Ideal Fluid Mechanics Equations Relying on Parallel Calculation of Multifluid Grids

In order to solve the numerical method of nonconservative ideal hydrodynamics equations, the viscous perturbation technique for solving nonconservative hydrodynamics equations is improved and tested by solving the Riemann problem. The calculation of nonconservative ideal fluid mechanics is based on the GRP format. This article aims at the calculation method of nonconservative ideal fluid mechanics in the GRP format. Riemann and the corresponding periodic vortex are processed. The multifluid network processing method in the article is compared with the current method. The result can prove that this format can be used to solve the nonconservative ideal fluid dynamics equation of multiple values in the GRP format group, its computing power is strong, and the result of the solution is accurate.

Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics

The numerical solution of relativistic hydrodynamics equations in conservative form requires root-finding algorithms that invert the conservative-to-primitive variables map. These algorithms employ the equation of state of the fluid and can be computationally demanding for applications involving sophisticated microphysics models, such as those required to calculate accurate gravitational wave signals in numerical relativity simulations of binary neutron stars. This work explores the use of machine learning methods to speed up the recovery of primitives in relativistic hydrodynamics. Artificial neural networks are trained to replace either the interpolations of a tabulated equation of state or directly the conservative-to-primitive map. The application of these neural networks to simple benchmark problems shows that both approaches improve over traditional root finders with tabular equation-of-state and multi-dimensional interpolations. In particular, the neural networks for the conservative-to-primitive map accelerate the variable recovery by more than an order of magnitude over standard methods while maintaining accuracy. Neural networks are thus an interesting option to improve the speed and robustness of relativistic hydrodynamics algorithms.

Application of Two-dimensional Finite Volume Method to Protoplanetary Disks

Many fascinating astrophysical phenomena can be simulated insufficiently by standard numerical schemes for the compressible hydrodynamics equations. In the present work, a high performant 2D hydrodynamical code has been developed. The model is designed for the planetary formation that consists of momentum, continuity and energy equations. Since the two-phase model seems to be hardly executed, we will show in a simplified form, the implementation of this model in one-phase. It is applied to the Solar System that such stars can form planets. The finite volume method (FVM) is used in this model. We aim to develop a first-order well-balanced scheme for the Euler equations in the the radial direction, combined with second-order centered ux following the radial direction. This conception is devoted to balance the uxes, and guarantee hydrostatic equilibrium preserving. Then the model is used on simplified examples in order to show its ca- pability to maintain steady-state solutions with a good precision. Additionally, we demonstrate the performance of the numerical code through simulations. In particularly, the time evolution of gas orbited around the star, and some proper- ties of the Rossby wave instability are analyzed. The resulting scheme shows consequently that this model is robust and simple enough to be easily implemented.

Neural Network Reconstruction of Plasma Space-Time

We explore the use of Physics-Informed Neural Networks (PINNs) for reconstructing full magnetohydrodynamic solutions from partial samples, mimicking the recreation of space-time environments around spacecraft observations. We use one-dimensional magneto- and hydrodynamic benchmarks, namely the Sod, Ryu-Jones, and Brio-Wu shock tubes, to obtain the plasma state variables along linear trajectories in space-time. These simulated spacecraft measurements are used as constraining boundary data for a PINN which incorporates the full set of one-dimensional (magneto) hydrodynamics equations in its loss function. We find that the PINN is able to reconstruct the full 1D solution of these shock tubes even in the presence of Gaussian noise. However, our chosen PINN transformer architecture does not appear to scale well to higher dimensions. Nonetheless, PINNs in general could turn out to be a promising mechanism for reconstructing simple magnetic structures and dynamics from satellite observations in geospace.

Regularity Criteria for the 3D Magneto-Hydrodynamics Equations in Anisotropic Lorentz Spaces

In this paper, we investigate the regularity of weak solutions to the 3D incompressible MHD equations. We provide a regularity criterion for weak solutions involving any two groups functions (∂1u1,∂1b1), (∂2u2,∂2b2) and (∂3u3,∂3b3) in anisotropic Lorentz space.

Impact of rotation on the evolution of convective vortices in collapsing stars

We study the impact of rotation on the hydrodynamic evolution of convective vortices during stellar collapse. Using linear hydrodynamics equations, we study the evolution of the vortices from their initial radii in convective shells down to smaller radii where they are expected to encounter the supernova shock. We find that the evolution of vortices is mainly governed by two effects: the acceleration of infall and the accompanying speed up of rotation. The former effect leads to the radial stretching of vortices, which limits the vortex velocities. The latter effect leads to the angular deformation of vortices in the direction of rotation, amplifying their non-radial velocity. We show that the radial velocities of the vortices are not significantly affected by rotation. We study acoustic wave emission and find that it is not sensitive to rotation. Finally, we analyze the impact of the corotation point and find that it has a small impact on the overall acoustic wave emission.