Space plasma simulations have seen an increase in the use of magnetohydrodynamic (MHD) with embedded Particle-in-Cell (PIC) models. This combined MHD-EPIC algorithm simulates some regions of interest using the kinetic PIC method while employing the MHD description in the rest of the domain. The MHD models are highly efficient and their fluid descriptions are valid for most part of the computational domain, thus making large-scale global simulations feasible.

However, in practical applications, the regions where the kinetic effects are critical can be changing, appearing, disappearing and moving in the computational domain. If a static PIC region is used, this requires a much larger PIC domain than actually needed, which can increase the computational cost dramatically.

To address the problem, we have developed a new method that is able to dynamically change the region of the computational domain where a PIC model is applied. We have implemented this new MHD with Adaptively Embedded PIC (MHD-AEPIC) algorithm using the BATS-R-US Hall MHD and the Adaptive Mesh Particle Simulator (AMPS) as the semi-implicit PIC models. We describe the algorithm and present a test case of two merging flux ropes to demonstrate its accuracy. The implementation uses dynamic allocation/deallocation of memory and load balancing for efficient parallel execution. We evaluate the performance of MHD-AEPIC compared to MHD-EPIC and the scaling properties of the model to large number of computational cores.

在空间等离子体模拟中，磁流体动力学 (MHD) 与嵌入式细胞内粒子 (PIC) 模型的使用有所增加。这种组合的 MHD-EPIC 算法使用动力学 PIC 方法模拟一些感兴趣的区域，同时在域的其余部分使用 MHD 描述。MHD 模型非常高效，并且它们的流体描述对于大部分计算域都是有效的，从而使大规模全局模拟变得可行。

然而，在实际应用中，动力学效应关键的区域可能会在计算域中发生变化、出现、消失和移动。如果使用静态 PIC 区域，则需要比实际需要大得多的 PIC 域，这会显着增加计算成本。

为了解决这个问题，我们开发了一种新方法，该方法能够动态改变应用 PIC 模型的计算域区域。我们使用 BATS-R-US Hall MHD 和自适应网格粒子模拟器 (AMPS) 作为半隐式 PIC 模型，通过自适应嵌入式 PIC (MHD-AEPIC) 算法实现了这种新 MHD。我们描述了该算法并展示了两个合并磁通绳的测试案例以证明其准确性。该实现使用内存的动态分配/解除分配和负载平衡来实现高效的并行执行。我们评估了 MHD-AEPIC 与 MHD-EPIC 相比的性能以及模型对大量计算核心的缩放特性。