arXiv subjects

Don Daniel

Publications and source records attributed to Don Daniel.

5 recordsLinked to original sources

arXiv2021

An asymptotic-preserving 2D-2P relativistic Drift-Kinetic-Equation solver for runaway electron simulations in axisymmetric tokamaks

We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated by analysis of the dominant numerical errors, as well as by numerical experiments. We demonstrate the ability of the algorithm to provide accurate answers regardless of plasma collisionality on a circular axisymmetric tokamak geometry.

physics.plasm-ph↗

arXiv2019

Optimal perturbations of gravitationally unstable, transient, boundary layers in porous media

We study gravitationally unstable, transient, diffusive boundary layers in porous media using modal and nonmodal stability methods. Using nonmodal stability theory, we demonstrate that both the onset of linear instabilities and the shape of optimal perturbations are highly sensitive to perturbation amplification measures and also the time at which the boundary layer is perturbed. This behavior is in contrast to traditional studies of steady or non-transient diffusive boundary layers where perturbation dynamics are independent of perturbation measure or time. We demonstrate that any analysis of transient layers produced through classical methods can result in physically unrealizable perturbation structures. To resolve the issue, we propose a nonmodal stability procedure which additionally constrains the perturbation dynamics to physically admissible fields. The proposed procedure predicts that instabilities grow primarily due to unstable perturbations featuring much larger spanwise wavenumbers (modes) and smaller amplifications compared to perturbations predicted using classical methods. We validate our predictions using direct numerical simulations that emulate the onset of convection in physical systems.

physics.flu-dyn↗

arXiv2019

Compressed Convolutional LSTM: An Efficient Deep Learning framework to Model High Fidelity 3D Turbulence

High-fidelity modeling of turbulent flows is one of the major challenges in computational physics, with diverse applications in engineering, earth sciences and astrophysics, among many others. The rising popularity of high-fidelity computational fluid dynamics (CFD) techniques like direct numerical simulation (DNS) and large eddy simulation (LES) have made significant inroads into the problem. However, they remain out of reach for many practical three-dimensional flows characterized by extremely large domains and transient phenomena. Therefore designing efficient and accurate data-driven generative approaches to model turbulence is a necessity. We propose a novel training approach for dimensionality reduction and spatio-temporal modeling of the three-dimensional dynamics of turbulence using a combination of Convolutional autoencoder and the Convolutional LSTM neural networks. The quality of the emulated turbulent fields is assessed with rigorous physics-based statistical tests, instead of visual assessments. The results show significant promise in the training methodology to generate physically consistent turbulent flows at a small fraction of the computing resources required for DNS.

physics.flu-dyn↗

arXiv2019

A fully implicit, scalable, conservative nonlinear relativistic Fokker-Planck 0D-2P solver for runaway electron

Upon application of a sufficiently strong electric field, electrons break away from thermal equilibrium and approach relativistic speeds. These highly energetic runaway electrons (MeV) play a significant role in tokamak disruption physics, and therefore their accurate understanding is essential to develop reliable mitigation strategies. For this purpose, we have developed a fully implicit solver for the 0D-2P (i.e., including two momenta coordinates) relativistic nonlinear Fokker-Planck equation (rFP). As in earlier implicit rFP studies (NORSE, CQL3D), electron-ion interactions are modeled using the Lorentz operator, and synchrotron damping using the Abraham-Lorentz-Dirac reaction term. However, our implementation improves on these earlier studies by 1) ensuring exact conservation properties for electron collisions, 2) strictly preserving positivity, and 3) being scalable algorithmically and in parallel. Key to our proposed approach is an efficient multigrid preconditioner for the linearized rFP equation, a multigrid elliptic solver for the Braams-Karney potentials [Braams and Karney, Phys. Rev. Lett. 59, 16 (1987)], and a novel adaptive technique to determine the associated boundary values. We verify the accuracy and efficiency of the proposed scheme with numerical results ranging from small electric-field electrical conductivity measurements to the accurate reproduction of runaway tail dynamics when strong electric fields are applied.

physics.comp-ph↗

arXiv2018

Reaction analogy based forcing for incompressible scalar turbulence

We present a novel reaction analogy (RA) based forcing method for generating stationary scalar fields in incompressible turbulence. The new method can produce more general scalar PDFs (e.g. double-delta) than current methods, while ensuring that scalar fields remain bounded. Such features are useful for generating initial fields in non-premixed combustion or for studying non-Gaussian scalar turbulence. The RA method mathematically models hypothetical chemical reactions that convert reactants in a mixed state back into its pure unmixed components. Various types of chemical reactions are formulated and the corresponding mathematical expressions derived such that the reaction term is smooth in the scalar space and is consistent with mass conservation. For large values of the scalar dissipation rate, the method produces statistically steady double-delta scalar PDFs. Quasi-uniform, Gaussian, and stretched exponential scalar statistics are recovered for smaller values of the scalar dissipation rate. The shape of the scalar PDF can be further controlled by changing the stoichiometric coefficients of the reaction. The ability of the new method to produce fully developed passive scalar fields with quasi-Gaussian PDFs is also investigated, by exploring the convergence of the third order mixed structure function to the "four-thirds" Yaglom's law.

physics.flu-dyn↗