Search results for "Equations"
showing 10 items of 955 documents
Numerical approximation of the viscous quantum hydrodynamic model for semiconductors
2006
The viscous quantum hydrodynamic equations for semiconductors with constant temperature are numerically studied. The model consists of the one-dimensional Euler equations for the electron density and current density, including a quantum correction and viscous terms, coupled to the Poisson equation for the electrostatic potential. The equations can be derived formally from a Wigner-Fokker-Planck model by a moment method. Two different numerical techniques are used: a hyperbolic relaxation scheme and a central finite-difference method. By simulating a ballistic diode and a resonant tunneling diode, it is shown that numerical or physical viscosity changes significantly the behavior of the solu…
Stochastic 0-dimensional Biogeochemical Flux Model: Effect of temperature fluctuations on the dynamics of the biogeochemical properties in a marine e…
2021
Abstract We present a new stochastic model, based on a 0-dimensional version of the well known biogeochemical flux model (BFM), which allows to take into account the temperature random fluctuations present in natural systems and therefore to describe more realistically the dynamics of real marine ecosystems. The study presents a detailed analysis of the effects of randomly varying temperature on the lower trophic levels of the food web and ocean biogeochemical processes. More in detail, the temperature is described as a stochastic process driven by an additive self-correlated Gaussian noise. Varying both correlation time and intensity of the noise source, the predominance of different plank…
The local boundedness of solutions for a class of degenerate nonlinear elliptic higher-order equations withL1-data
2008
We prove local boundedness of solutions for a class of degenerate nonlinear elliptic higher-order equations with L(1)-data.
Power ENO methods: a fifth-order accurate Weighted Power ENO method
2004
In this paper we introduce a new class of ENO reconstruction procedures, the Power ENO methods, to design high-order accurate shock capturing methods for hyperbolic conservation laws, based on an extended class of limiters, improving the behavior near discontinuities with respect to the classical ENO methods. Power ENO methods are defined as a correction of classical ENO methods [J. Comput. Phys. 71 (1987) 231], by applying the new limiters on second-order differences or higher. The new class of limiters includes as a particular case the minmod limiter and the harmonic limiter used for the design of the PHM methods [see SIAM J. Sci. Comput. 15 (1994) 892]. The main features of these new ENO…
Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation
2017
In this paper we will present and analyze a new class of the IMEX finite volume schemes for the Euler equations with a gravity source term. We will in particular concentrate on a singular limit of weakly compressible flows when the Mach number M1. In order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gravity waves and a non-stiff nonlinear part that models nonlinear advection effects. For time discretization we use a special class of the so-called globally stiffly accurate IMEX schemes and approximate the stiff linear operator implicitly and the non-stiff nonlinear operator explicitly. For spatial discretization t…
Electrophoretic properties of charged colloidal suspensions: Application of a hybrid MD/LB method
2006
Abstract Electrophoretic properties of charged colloidal suspensions are investigated using a hybrid simulation method. In this method, the colloidal particles are propagated via Newton’s equations of motion using molecular dynamics (MD), while they are coupled to a structureless solvent that is modelled by the Lattice-Boltzmann (LB) method.
Efficient numerical methods for pricing American options under stochastic volatility
2007
Five numerical methods for pricing American put options under Heston's stochastic volatility model are described and compared. The option prices are obtained as the solution of a two-dimensional parabolic partial differential inequality. A finite difference discretization on nonuniform grids leading to linear complementarity problems with M-matrices is proposed. The projected SOR, a projected multigrid method, an operator splitting method, a penalty method, and a componentwise splitting method are considered. The last one is a direct method while all other methods are iterative. The resulting systems of linear equations in the operator splitting method and in the penalty method are solved u…
Comparison between adaptive and uniform discontinuous Galerkin simulations in dry 2D bubble experiments
2013
Accepted by the Journal of Computational Physics Adaptive mesh refinement generally aims to increase computational efficiency without compromising the accuracy of the numerical solution. However it is an open question in which regions the spatial resolution can actually be coarsened without affecting the accuracy of the result. This question is investigated for a specific example of dry atmospheric convection, namely the simulation of warm air bubbles. For this purpose a novel numerical model is developed that is tailored towards this specific application. The compressible Euler equations are solved with a Discontinuous Galerkin method. Time integration is done with an IMEXmethod and the dy…
Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach
2015
Due to errors in measurements and inherent variability in the quantities of interest, models based on random differential equations give more realistic results than their deterministic counterpart. The generalized polynomial chaos (gPC) is a powerful technique used to approximate the solution of these equations when the random inputs follow standard probability distributions. But in many cases these random inputs do not have a standard probability distribution. In this paper, we present a step-by-step constructive methodology to implement directly a useful version of adaptive gPC for arbitrary distributions, extending the applicability of the gPC. The paper mainly focuses on the computation…
Fractional differential equations solved by using Mellin transform
2014
In this paper, the solution of the multi-order differential equations, by using Mellin Transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the Mellin integral operates on the fractional derivatives, may be overcame. Then, the solution may be found for any fractional differential equation involving multi-order fractional derivatives (or integrals). The solution is found in the Mellin domain, by solving a linear set of algebraic equations, whose inverse transform gives the solution of the fractional differential equation at hands.