Search results for "Solver"
showing 10 items of 157 documents
Systematic Approach To Calculate the Concentration of Chemical Species in Multi-Equilibrium Problems
2010
A general systematic approach is proposed for the numerical calculation of multi-equilibrium problems. The approach involves several steps: (i) the establishment of balances involving the chemical species in solution (e.g., mass balances, charge balance, and stoichiometric balance for the reaction products), (ii) the selection of the unknowns (the concentration of selected chemical species at equilibrium), (iii) the estimation of the concentration of the other species based on the selected species and the equilibrium expressions, and (iv) the minimization of the sum of the squared balances (search of the optimal combination of the unknowns). The application of the systematic approach to cas…
A Numerical Study of Relativistic Jets
1996
Numerical simulations of supersonic jets are able to explain the structures observed in many VLA images of radio sources. The improvements achieved in classical simulations (see Hardee, these proceedings) are in contrast with the almost complete lack of relativistic simulations the reason being that numerical difficulties arise from the highly relativistic flows typical of extragalactic jets. For our study, we have developed a two-dimensional code which is based on (i) an explicit conservative differencing of the special relativistic hydrodynamics (SRH) equations and (ii) the use of an approximate Riemann solver (see Marti et al. 1995a,b and references therein).
Fast Direct Solver for a Time-harmonic Electromagnetic Problem with an Application
2003
A fast direct solution of a periodic problem derived from the time-harmonic Maxwell’s equations is considered. The problem is discretized by low order hexahedral finite elements proposed by Nedelec. The solver is based on the application of FFT, and it has the computational cost O(N log N). An application to scattering of an electromagnetic wave by a periodic structure is presented.
On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes
2016
We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfven waves, and the tearing mode instability using the MHD code Aenus. By comparing the simu- lation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of tearing modes we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast-magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) syst…
3D Relativistic Hydrodynamics
2007
We review the evolution of the numerical techniques applied in relativistic hydrodynamics since the sixties until today. We focus our attention on the state-of- the-art high-resolution shock-capturing methods and the astrophysical applications involving three-dimensional simulations.
Relativistic Magnetohydrodynamics: Renormalized eigenvectors and full wave decomposition Riemann solver
2010
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wavefront in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as…
A new multidimensional, energy-dependent two-moment transport code for neutrino-hydrodynamics
2015
We present the new code ALCAR developed to model multidimensional, multi energy-group neutrino transport in the context of supernovae and neutron-star mergers. The algorithm solves the evolution equations of the 0th- and 1st-order angular moments of the specific intensity, supplemented by an algebraic relation for the 2nd-moment tensor to close the system. The scheme takes into account frame-dependent effects of order O(v/c) as well as the most important types of neutrino interactions. The transport scheme is significantly more efficient than a multidimensional solver of the Boltzmann equation, while it is more accurate and consistent than the flux-limited diffusion method. The finite-volum…
A fast solver for nonlocal electrostatic theory in biomolecular science and engineering
2011
Biological molecules perform their functions surrounded by water and mobile ions, which strongly influence molecular structure and behavior. The electrostatic interactions between a molecule and solvent are particularly difficult to model theoretically, due to the forces' long range and the collective response of many thousands of solvent molecules. The dominant modeling approaches represent the two extremes of the trade-off between molecular realism and computational efficiency: all-atom molecular dynamics in explicit solvent, and macroscopic continuum theory (the Poisson or Poisson--Boltzmann equation). We present the first fast-solver implementation of an advanced nonlocal continuum theo…
Monte Carlo Simulation of Harmonic Generation in GaAs structures operating under large-signal Conditions
2007
By using a multiparticles Monte Carlo technique, with a self-consistently coupled one-dimensional Poisson solver, we investigate the dependence of the nonlinear carrier dynamics in GaAs n+nn+ micro e submicro-structures operating under very intense sub-terahertz signals by: (i) the frequency and the intensity of the excitation signal and (ii) the length of the n region.
Isospin-invariant Skyrme energy-density-functional approach with axial symmetry
2014
We develop the isospin-invariant Skyrme-EDF method by considering local densities in all possible isospin channels and proton-neutron (p-n) mixing terms as mandated by the isospin symmetry. The EDF employed has the most general form that depends quadratically on the isoscalar and isovector densities. We test and benchmark the resulting p-n EDF approach, and study the general properties of the new scheme by means of the cranking in the isospin space. We extend the existing axial DFT solver HFBTHO to the case of isospin-invariant EDF approach with all possible p-n mixing terms. Explicit expressions have been derived for all the densities and potentials that appear in the isospin representatio…