arXiv subjects

Oleksandr Koshkarov

Publications and source records attributed to Oleksandr Koshkarov.

10 recordsLinked to original sources

arXiv2026

Novel approach to general curvilinear coordinates for plasma fluid applications

In general geometry, plasma fluid equations include nonlinear geometric sources associated with fictitious forces, which pose significant challenges to computer simulations. We reformulate the plasma fluid hierarchy to rigorously preserve geometry and conservation properties critical to numerical simulations, while concealing the geometric sources. In their discrete form, the reformulated models conserve mass, angular momentum, and energy naturally, by simple analogy with the continuum equations. These conservation properties have minimal requirements in discrete space, namely, the anti-symmetry of the first derivative and the orthogonality of the scalar and cross products. By decoupling magnetic geometry, coordinate systems, and numerical discretization, this enables maximum flexibility while preserving physics fidelity. As a testbed, we apply the novel representation to the resistive magnetohydrodynamic system, which involves a complete set of curvilinear operations. We verify the correctness of the approach using steady state liquid metal flows and the classic Orszag-Tang vortex.

physics.plasm-ph↗

arXiv2025

Conservative projection-based data-driven model order reduction of a fluid-kinetic spectral solver

Kinetic simulations are computationally intensive due to six-dimensional phase space discretization. Many kinetic spectral solvers use the asymmetrically weighted Hermite expansion due to its conservation and fluid-kinetic coupling properties, i.e., the lower-order Hermite moments capture and describe the macroscopic fluid dynamics and higher-order Hermite moments describe the microscopic kinetic dynamics. We leverage this structure by developing a parametric data-driven reduced-order model based on the proper orthogonal decomposition, which projects the higher-order kinetic moments while retaining the fluid moments intact. This approach can also be understood as learning a nonlocal closure via a reduced modal decomposition. We demonstrate analytically and numerically that the method ensures local and global mass, momentum, and energy conservation. The numerical results show that the proposed method effectively replicates the high-dimensional spectral simulations at a fraction of the computational cost and memory, as validated on the weak Landau damping and two-stream instability benchmark problems.

physics.plasm-ph↗

arXiv2025

Effects of Artificial Collisions, Filtering, and Nonlocal Closure Approaches on Hermite-based Vlasov-Poisson Simulations

Kinetic simulations of collisionless plasmas are computationally challenging due to phase space mixing and filamentation, resulting in fine-scale velocity structures. This study compares three methods developed to reduce artifacts related to limited velocity resolution in Hermite-based Vlasov-Poisson simulations: artificial collisions, filtering, and nonlocal closure approaches. We evaluate each method's performance in approximating the linear kinetic response function and suppressing recurrence in linear and nonlinear regimes. Numerical simulations of Landau damping demonstrate that artificial collisions, particularly higher orders of the Lenard-Bernstein collisional operator, most effectively recover the correct damping rate across a range of wavenumbers. Moreover, Hou-Li filtering and nonlocal closures underdamp high wavenumber modes in linear simulations, and the Lenard- Bernstein collisional operator overdamps low wavenumber modes in both linear and nonlinear simulations. This study demonstrates that hypercollisions offer a robust approach to kinetic simulations, accurately capturing collisionless dynamics with limited velocity resolution.

physics.plasm-ph↗

arXiv2024

Conservative Closures of the Vlasov-Poisson Equations Based on Symmetrically Weighted Hermite Spectral Expansion

We derive conservative closures of the Vlasov-Poisson equations discretized in velocity via the symmetrically weighted Hermite spectral expansion. The short note analyzes the conservative closures preservation of the hyperbolicity and anti-symmetry of the Vlasov equation. Furthermore, we verify numerically the analytically derived conservative closures on simulating a classic electrostatic benchmark problem: the Langmuir wave. The numerical results and analytic analysis show that the closure by truncation is the most suitable conservative closure for the symmetrically weighted Hermite formulation.

physics.comp-ph↗

arXiv2024

Anti-symmetric and Positivity Preserving Formulation of a Spectral Method for Vlasov-Poisson Equations

We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions, central finite differencing in space, and an implicit Runge Kutta integrator in time. The proposed discretization preserves the anti-symmetric structure of the advection operator in the Vlasov equation, resulting in a stable numerical method. We apply such discretization to two formulations: the canonical Vlasov-Poisson equations and their continuously transformed square-root representation. The latter preserves the positivity of the particle distribution function. We derive analytically the conservation properties of both formulations, including particle number, momentum, and energy, which are verified numerically on the following benchmark problems: manufactured solution, linear and nonlinear Landau damping, two-stream instability, bump-on-tail instability, and ion-acoustic wave.

math.NA↗

arXiv2024

Scale Separation Effects on Simulations of Plasma Turbulence

Understanding plasma turbulence requires a synthesis of experiments, observations, theory, and simulations. In the case of kinetic plasmas such as the solar wind, the lack of collisions renders the fluid closures such as viscosity meaningless and one needs to resort to higher order fluid models or kinetic models. Typically, the computational expense in such models is managed by simulating artificial values of certain parameters such as the ratio of the Alfvén speed to the speed of light ($v_A/c$) or the relative mass ratio of ions and electrons ($m_i/m_e$). Although, typically care is taken to use values as close as possible to realistic values within the computational constraints, these artificial values could potentially introduce unphysical effects. These unphysical effects could be significant at sub-ion scales, where kinetic effects are the most important. In this paper, we use the ten-moment fluid model in the Gkeyll framework to perform controlled numerical experiments, systematically varying the ion-electron mass ratio from a small value down to the realistic proton-electron mass ratio. We show that the unphysical mass ratio has a significant effect on the kinetic range dynamics as well as the heating of both the plasma species. The dissipative process for both ions and electrons become more compressive in nature, although the ions remain nearly incompressible in all cases. The electrons move from being dominated by incompressive viscous like heating/dissipation, to very compressive heating/dissipation dominated by compressions/rarefactions. While the heating change is significant for the electrons, a mass ratio of $m_i/m_e \sim 250$ captures the asymptotic behaviour of electron heating.

physics.plasm-ph↗

arXiv2024

On a spectral method for $β$-particle bound excitation collisions in kilonovae

The interaction of $β$-particles with the weakly ionized plasma background is an important mechanism for powering the kilonova transient signal from neutron star mergers. For this purpose, we present an implementation of the approximate fast-particle collision kernel, described by Inokuti (1971) following the seminal formulation of Bethe (1930), in a spectral solver of the Vlasov-Maxwell-Boltzmann equations. In particular, we expand the fast-particle plane-wave atomic excitation kernel into coefficients of the Hermite basis, and derive the relevant discrete spectral system. In this fast-particle limit, the approach permits the direct use of atomic data, including optical oscillator strengths, normally applied to photon-matter interaction. The resulting spectral matrix is implemented in the MASS-APP spectral solver framework, in a way that avoids full matrix storage per spatial zone. We numerically verify aspects of the matrix construction, and present a proof-of-principle 3D simulation of a 2D axisymmetric kilonova ejecta snapshot. Our preliminary numerical results indicate that a reasonable choice of Hermite basis parameters for $β$-particles in the kilonova are a bulk velocity parameter $\vec{u}=0$, a thermal velocity parameter $\vecα=0.5c$, and a 9x9x9 mode velocity basis set (Hermite orders 0 to 8 in each dimension). For ejecta-interior sample zones, we estimate the ratio of thermalization from large-angle ($\gtrsim2.5^{\circ}$) bound excitation scattering to total thermalization is $\sim$0.002-0.003.

astro-ph.HE↗

arXiv2022

Energy-conserving explicit and implicit time integration methods for the multi-dimensional Hermite-DG discretization of the Vlasov-Maxwell equations

We study the conservation properties of the Hermite-discontinuous Galerkin (Hermite-DG) approximation of the Vlasov-Maxwell equations. In this semi-discrete formulation, the total mass is preserved independently for every plasma species. Further, an energy invariant exists if central numerical fluxes are used in the DG approximation of Maxwell's equations, while a dissipative term is present when upwind fluxes are employed. In general, traditional temporal integrators might fail to preserve invariants associated with conservation laws during the time evolution. Hence, we analyze the capability of explicit and implicit Runge-Kutta (RK) temporal integrators to preserve such invariants. Since explicit RK methods can only ensure preservation of linear invariants but do not provide any control on the system energy, we consider modified explicit RK methods in the family of relaxation Runge-Kutta methods (RRK). These methods can be tuned to preserve the energy invariant at the continuous or semi-discrete level, a distinction that is important when upwind fluxes are used in the discretization of Maxwell's equations since upwind provides a numerical source of energy dissipation that is not present when central fluxes are used. We prove that the proposed methods are able to preserve the energy invariant and to maintain the semi-discrete energy dissipation (if present) according to the discretization of Maxwell's equations. An extensive set of numerical experiments corroborates the theoretical findings. It also suggests that maintaining the semi-discrete energy dissipation when upwind fluxes are used leads to an overall better accuracy of the method relative to using upwind fluxes while forcing exact energy conservation.

math.NA↗

arXiv2020

The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov-Maxwell equations

We discuss the development, analysis, implementation, and numerical assessment of a spectral method for the numerical simulation of the three-dimensional Vlasov-Maxwell equations. The method is based on a spectral expansion of the velocity space with the asymmetrically weighted Hermite functions. The resulting system of time-dependent nonlinear equations is discretized by the discontinuous Galerkin (DG) method in space and by the method of lines for the time integration using explicit Runge-Kutta integrators. The resulting code, called Spectral Plasma Solver (SPS-DG), is successfully applied to standard plasma physics benchmarks to demonstrate its accuracy, robustness, and parallel scalability.

physics.comp-ph↗

arXiv2017

Generalized lower-hybrid mode with, density gradient, equilibrium ExB drift, collisions and finite electron Larmor radius: Numerical studies with MATLAB solver

MATLAB solver for general dispersion relation has been developed to study local instabilities in partially magnetized plasmas typical for ExB discharges. Several examples of the Simon-Hoh, lower-hybrid and ion-sound instabilities with the parameters typical for Penning discharge are shown. This solver allows parametrically investigate the local dispersion relation for the wide range of plasma parameters and prepare reports.

physics.plasm-ph↗