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Wereportonanewmultiscalemethodapproachforthestudyofsystemswith wide separation of short-range forces acting on short time scales and long-range forces acting on much slower scales. We consider the case of the Poisson-Boltzmann equation that describes the long-range forces using the Boltzmann formula (i.e. we assume the medium to be in quasi local thermal equilibrium). We developed a new approach where fields and particle information (mediated by the equations for their moments) are solved self-consistently. The new approach is implicit and numerically stable, providing exact energy conservation. We tested different implementations all leading to exact energy conservation. The new method requires the solution of a large set of non-linear equations. We considered three solution strategies: Jacobian Free Newton Krylov, an alternative, called field hiding, based on hiding part of the residual calculation and replacing them with direct solutions and a Direct Newton Schwarz solver that considers simplified single particle-based Jacobian. The field hiding strategy proves to be the most efficient approach.
Recently, a family of models that couple multifluid systems to the full Maxwell equations draw a lot of attention in laboratory, space, and astrophysical plasma modeling. These models are more complete descriptions of the plasma than reduced models l
Based on the previously developed Energy Conserving Semi Implicit Method (ECsim) code, we present its cylindrical implementation, called ECsim-CYL, to be used for axially symmetric problems. The main motivation for the development of the cylindrical
This work presents new parallelizable numerical schemes for the integration of Dissipative Particle Dynamics with Energy conservation (DPDE). So far, no numerical scheme introduced in the literature is able to correctly preserve the energy over long
This work further improves the pseudo-transient approach for the Poisson Boltzmann equation (PBE) in the electrostatic analysis of solvated biomolecules. The numerical solution of the nonlinear PBE is known to involve many difficulties, such as expon
We describe how regularization of lattice Boltzmann methods can be achieved by modifying dissipation. Classes of techniques used to try to improve regularization of LBMs include flux limiters, enforcing the exact correct production of entropy and man