A new SPH-based MHD code SPMHD

A new Smoothed Particle Magnetohydrodynamics (SPMHD) code that combines smoothed particle hydrodynamics (SPH) and finite element method (FEM) has been developed to accurately simulate the motion of fluids and electromagnetic fields. This hybrid approach allows for a more comprehensive simulation of magnetohydrodynamic phenomena, especially at plasma/vacuum interface, by separately treating the fluid motion (by SPH module) and the electromagnetic field dynamics (by FEM module). The SPH module of the code excels in handling fluid dynamics, including large deformations, fluid instabilities, fluid-solid boundary interactions, shock capturing, and plasma properties. Its robust formulation enables accurate modeling of complex fluid behaviors and interactions. On the other hand, the FEM module of the SPMHD code is capable of handling complex geometry, ensuring magnetic field conservation by solving the equations for magnetic vector potential and electric scalar potential, and globally solving the current density in electrodes and moving plasma. The coupling between SPH and FEM in the SPMHD code is achieved through an operator splitting method. This capability enables the accurate representation of electromagnetic phenomena and their interactions with the fluid, enabling real-time coupling of magneticelectric-thermal-fluid fields. To validate the capabilities of the SPMHD code, we present benchmark tests and compare the results with analytical solutions and other numerical codes. The blow-by instability simulations demonstrate the accuracy and efficiency of the hybrid SPH-FEM approach in capturing the complex interplay between fluid dynamics and magnetic field behavior. The SPMHD code is designed for three-dimensional simulations, exhibits high MPI parallelism, robustness and reliability throughout the simulation process. All the features of the SPMHD code make it suitable for a wide range of applications in plasma physics, astrophysics, and engineering.