- Ferrara, Emilia-Romagna, Italy
lorenzo pareschi
Ferrara, Mathematics, Department Member
Research Interests:
Research Interests: Nonlinear hyperbolic equations, Heat Transfer, Numerical Analysis, Stability, Numerical Method, and 12 moreKinetic Theory, Singular perturbation problems, PARTIAL DIFFERENTIAL EQUATION, Dissipation, Parabolic Wave Equation, High Resolution, Historic conservation law, Acoustic Diffusion Equation Model, Boltzmann equation, Numerical Analysis and Computational Mathematics, Asymptotic Behavior, and Reynolds Number
Abstract In order to embark the development of characteristic based schemes for hyperbolic systems with nonlinear sti source terms we have studied a prototype one-dimensional discrete-velocity Boltzmann equation. We show that the method... more
Abstract In order to embark the development of characteristic based schemes for hyperbolic systems with nonlinear sti source terms we have studied a prototype one-dimensional discrete-velocity Boltzmann equation. We show that the method can be evaluated at the cost of an explicit scheme and that yield accurate solutions even when the relaxation time is much less than the time step. Numerical experiments con rm that the quality of the results obtained is comparable with those of earlier approaches.
Research Interests:
Research Interests:
In this work, a new formulation for central schemes based on staggered grids is proposed. It is based on a novel approach in which first a time discretization is carried out, followed by the space discretization. The schemes obtained in... more
In this work, a new formulation for central schemes based on staggered grids is proposed. It is based on a novel approach in which first a time discretization is carried out, followed by the space discretization. The schemes obtained in this fashion have a simpler structure than previous central schemes. For high order schemes, this simplification results in higher computational efficiency. In this work, schemes of order 2 to 5 are proposed and tested, although central Runge--Kutta schemes of any order of accuracy can be constructed in ...
Research Interests:
Research Interests: Conservation, Monte Carlo, Heat Transfer, Media, Mixing, and 28 moreDiffusion, System, Relaxation, Non Linear Dynamics, Laminar Microflows, Quadrature, PARTIAL DIFFERENTIAL EQUATION, Difusion, Accuracy, Wave Equation, Parabolic Wave Equation, Steady state, High Resolution, Historic conservation law, WAve, Equilibrium, Radiative Transfer, Acoustic Diffusion Equation Model, Precision, Granular Media, Parity, Boundary Value Problem, Magnitude, Lattice Boltzmann Equations, Transport Equation, Milieu, Relaxation Scheme, and Continuo
In this paper we show that the use of spectral Galerkin methods for the approximation of the Boltzmann equation in the velocity space permits one to obtain spectrally accurate numerical solutions at a reduced computational cost. We prove... more
In this paper we show that the use of spectral Galerkin methods for the approximation of the Boltzmann equation in the velocity space permits one to obtain spectrally accurate numerical solutions at a reduced computational cost. We prove that the spectral algorithm preserves the total mass and approximates with infinite-order accuracy momentum and energy. Consistency of the method is also proved, and a stability result for a smoothed positive scheme is given. We demonstrate that the Fourier coefficients associated with the ...
Research Interests:
Research Interests: Monte Carlo, Numerical Analysis, Kinetic Modeling, Mixing, Non Linear Dynamics, and 15 moreLaminar Microflows, Porous media equation, Navier Stokes, Parabolic Wave Equation, Historic conservation law, Boltzmann equation, Numerical Analysis and Computational Mathematics, Granular Media, Lumping Kinetic Model, Two Dimensions, Lattice Boltzmann Equations, Burgers equation, Heat Equation, Kinetic Equation, and Relaxation Scheme
We consider new implicit–explicit (IMEX) Runge–Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability-preserving (SSP) scheme, and the implicit part is... more
We consider new implicit–explicit (IMEX) Runge–Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability-preserving (SSP) scheme, and the implicit part is treated by an L-stable diagonally implicit Runge–Kutta method (DIRK). The schemes proposed are asymptotic preserving (AP) in the zero relaxation limit. High accuracy in space is obtained by Weighted Essentially Non Oscillatory (WENO) reconstruction. After a description of the mathematical properties of the schemes, several applications will be presented
Research Interests:
In this paper, we discuss the large-time behavior of solution of a simple kinetic model of Boltzmann–Maxwell type, such that the temperature is time decreasing and/or time increasing. We show that, under the combined effects of the... more
In this paper, we discuss the large-time behavior of solution of a simple kinetic model of Boltzmann–Maxwell type, such that the temperature is time decreasing and/or time increasing. We show that, under the combined effects of the nonlinearity and of the time-monotonicity of the temperature, the kinetic model has non trivial quasi-stationary states with power law tails. In order to do this we consider a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the distribution. The same idea is applied to investigate the large-time behavior of an elementary kinetic model of economy involving both exchanges between agents and increasing and/or decreasing of the mean wealth. In this last case, the large-time behavior of the solution shows a Pareto power law tail. Numerical results confirm the previous analysis.
Research Interests:
Research Interests:
In this paper we study the numerical passage from the spatially homogeneous Boltzmann equation without cut-off to the Fokker-Planck-Landau equation in the so-called grazing collision limit. To this aim we derive a Fourier spectral method... more
In this paper we study the numerical passage from the spatially homogeneous Boltzmann equation without cut-off to the Fokker-Planck-Landau equation in the so-called grazing collision limit. To this aim we derive a Fourier spectral method for the non cut-off Boltzmann equation in the spirit of [21,23]. We show that the kernel modes that define the spectral method have the correct grazing collision limit providing a consistent spectral method for the limiting Fokker-Planck-Landau equation. In particular, for small values of the scattering angle, we derive an approximate formula for the kernel modes of the non cut-off Boltzmann equation which, similarly to the Fokker-Planck-Landau case, can be computed with a fast algorithm. The uniform spectral accuracy of the method with respect to the grazing collision parameter is also proved.
Research Interests: Applied Mathematics, Mathematical Physics, Plasma Physics, Statistical Mechanics, Spectral Methods, and 9 moreNumerical Analysis, Fourier Analysis, APPROXIMATION ALGORITHM, Spectral method, FOkker Planck Equation, PARTIAL DIFFERENTIAL EQUATION, Boltzmann equation, Numerical Analysis and Computational Mathematics, and Transport Equation
Research Interests:
In this work, a new formulation for central schemes based on staggered grids is proposed. It is based on a novel approach in which first a time discretization is carried out, followed by the space discretization. The schemes obtained in... more
In this work, a new formulation for central schemes based on staggered grids is proposed. It is based on a novel approach in which first a time discretization is carried out, followed by the space discretization. The schemes obtained in this fashion have a simpler structure than previous central schemes. For high order schemes, this simplification results in higher computational efficiency. In this work, schemes of order 2 to 5 are proposed and tested, although central Runge--Kutta schemes of any order of accuracy can be constructed in ...
Research Interests:
A new family of Monte Carlo schemes is introduced for the numerical solution of the Boltzmann equation of rarefied gas dynamics. The schemes are inspired by the Wild sum expansion of the solution of the Boltzmann equation for Maxwellian... more
A new family of Monte Carlo schemes is introduced for the numerical solution of the Boltzmann equation of rarefied gas dynamics. The schemes are inspired by the Wild sum expansion of the solution of the Boltzmann equation for Maxwellian molecules and consist of a novel time discretization of the equation. In particular, high order terms in the expansion are replaced by the equilibrium Maxwellian distribution. The two main features of the schemes are high order accuracy in time and asymptotic preservation. The first property ...
Research Interests: Applied Mathematics, Molecular Dynamics Simulation, Monte Carlo Simulation, Monte Carlo, Statistical Physics, and 12 moreFluid Dynamics, Statistical Physics Of Complex Systems, Monte Carlo Methods, Gas Dynamics, Euler Equations, Boltzmann equation, Euler Lagrange Equation, Numerical Analysis and Computational Mathematics, Shock Wave, High Order Accuracy, Numerical Solution, and Monte Carlo Method
Abstract In this paper we introduce a new smoothed scheme derived from the spectral Fourier method for the homogeneous Boltzmann equation recently introduced in [14, 15]. More precisely we show that using suitable smoothing filters the... more
Abstract In this paper we introduce a new smoothed scheme derived from the spectral Fourier method for the homogeneous Boltzmann equation recently introduced in [14, 15]. More precisely we show that using suitable smoothing filters the method can be designed in such a way that the spectral solution remains positive in time and preserves the total mass. Several numerical examples are given to illustrate the previous analysis.