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We present a new polynomial-free prolongation scheme for Adaptive Mesh Re- finement (AMR) simulations of compressible and incompressible computational fluid dynamics. The new method is constructed using a multi-dimensional kernel-based Gaussian Process (GP) prolongation model. The formulation for this scheme was inspired by the two previous studies on the GP methods in- troduced by A. Reyes et al., Journal of Scientific Computing, 76 (2017), and Journal of Computational Physics, 381 (2019). In this paper, we extend the previous GP interpolations and reconstructions to a new GP-based AMR pro- longation method that delivers a third-order accurate prolongation of data from coarse to fine grids on AMR grid hierarchies. In compressible flow simulations, special care is necessary to handle shocks and discontinuities in a stable man- ner. To meet this, we utilize the shock handling strategy using the GP-based smoothness indicators developed in the previous GP work by A. Reyes et al. We compare our GP-AMR results with the test results using the second-order linear AMR method to demonstrate the efficacy of the GP-AMR method in a series of test suite problems using the AMReX library, in which the GP-AMR method has been implemented. 

Heat conduction is strongly suppressed in turbulent, weakly collisional, and magnetized plasmas. 

Understanding magnetic-field generation and amplification in turbulent plasma is essential to account for observations of magnetic fields in the universe. A theoretical framework attributing the origin and sustainment of these fields to the so-called fluctuation dynamo was recently validated by experiments on laser facilities in low-magnetic-Prandtl-number plasmas ( P m < 1 ). However, the same framework proposes that the fluctuation dynamo should operate differently when P m ≳ 1 , the regime relevant to many astrophysical environments such as the intracluster medium of galaxy clusters. This paper reports an experiment that creates a laboratory P m ≳ 1 plasma dynamo. We provide a time-resolved characterization of the plasma’s evolution, measuring temperatures, densities, flow velocities, and magnetic fields, which allows us to explore various stages of the fluctuation dynamo’s operation on seed magnetic fields generated by the action of the Biermann-battery mechanism during the initial drive-laser target interaction. The magnetic energy in structures with characteristic scales close to the driving scale of the stochastic motions is found to increase by almost three orders of magnitude and saturate dynamically. It is shown that the initial growth of these fields occurs at a much greater rate than the turnover rate of the driving-scale stochastic motions. Our results point to the possibility that plasma turbulence produced by strong shear can generate fields more efficiently at the driving scale than anticipated by idealized magnetohydrodynamics (MHD) simulations of the nonhelical fluctuation dynamo; this finding could help explain the large-scale fields inferred from observations of astrophysical systems.