Projection Methods for Multiscale Problems in Plasma Physics and Applications

Chorin和Tokman的研究人员开发的数值方法在对等离子体动力学中明显的多尺度现象的长期模拟中将是有效的，特别是在模拟磁重联方面。他们还在日冕的等离子体动力学研究和实验室实验中使用这种方法。他们提供了这些方法的软件实现。该方法将投影技术与指数传播型格式相结合进行时间推进。在天体物理和实验室等离子体中看到的动力学行为是复杂的，要理解它需要计算机模拟。但感兴趣的现象跨越了广泛的时间长度和时间尺度。因此，为了准确地计算描述这些现象的方程的解，传统的数值方法需要在很长的时间周期内进行很小的时间步长。同样，精确的解的空间分辨率需要精细的空间网格。总而言之，这些因素需要在每个时间步长上求解非常大的方程系统，在许多时间步长上。这样的计算成本很高。研究人员开发和分析了承诺降低计算成本的数值方法，并将其应用于研究等离子体物理问题。它们使这种方法在软件中可用。这扩大了这项工作的潜在影响，因为在各种科学和工程应用中都会出现多个尺度的问题。

Chorin and Tokman The investigators develop numerical methods that will beeffective in long-time simulations of the multi-scale phenomenaevident in plasma dynamics, particularly in modeling magneticreconnection. They also use the methods in studies of plasmadynamics in the solar corona and in laboratory experiments. Theymake available a software implementation of the methods. Themethods combine projection techniques with schemes of exponentialpropagation type for time-stepping. The dynamical behavior seen in astrophysical and laboratoryplasmas is complicated, and to understand it requires computersimulations. But the phenomena of interest span a wide range oflength and time scales. Consequently, to compute accurately thesolutions of the equations that describe these phenomena,conventional numerical methods require small steps in time oververy long time periods. Similarly, accurate spatial resolution ofthe solutions requires fine spatial meshes. Together, thesefactors require solving very large systems of equations at eachtime step, for a great many time steps. Such calculations areexpensive. The investigators develop and analysze numericalmethods that promise to reduce the computational costs, and applythem to study plasma physics problems. They make the methodsavailable in software. This widens the potential impact of thework, because problems with multiple scales arise in a variety ofscience and engineering applications.