scholarly journals Numerical integration of the axisymmetric Robinson-Trautman equation by a spectral method

1999 ◽  
Vol 41 (2) ◽  
pp. 271-280 ◽  
Author(s):  
D. A. Prager ◽  
A. W.-C. Lun
Keyword(s):  
Numerical Integration ◽  
Spectral Decomposition ◽  
Finite Difference Schemes ◽  
Qualitative Comparison ◽  
Transform Method ◽  
Higher Order Modes ◽  
Spectral Transform ◽  
Long Time ◽  
Bondi Mass ◽  
Meteorological Problems

AbstractWe have adapted the Spectral Transform Method, a technique commonly used in non-linear meteorological problems, to the numerical integration of the Robinson-Trautman equation. This approach eliminates difficulties due to the S2 × R+ topology of the equation. The method is highly accurate for smooth data and is numerically robust. Under spectral decomposition the long-time equilibrium state takes a particularly simple form: all nonlinear (l ≥ 2) modes tend to zero. We discuss the interaction and eventual decay of these higher order modes, as well as the evolution of the Bondi mass and other derived quantities. A qualitative comparison between the Spectral Transform Method and two finite difference schemes is given.

Stress Drop Derived from Spectral Analysis Considering the Hypocentral Depth in the Attenuation Model: Application to the Ridgecrest Region, California

2021 ◽  
Author(s):  
Dino Bindi ◽  
Hoby N. T. Razafindrakoto ◽  
Matteo Picozzi ◽  
Adrien Oth
Keyword(s):  
Stress Drop ◽  
Spectral Decomposition ◽  
Epicentral Distance ◽  
Source Parameters ◽  
S Wave ◽  
Qualitative Comparison ◽  
Ground Shaking ◽  
Attenuation Model ◽  
Hypocentral Distance ◽  
The Impact

ABSTRACT We investigate the impact of considering a depth-dependent attenuation model on source parameters assessed through a spectral decomposition. In particular, we evaluate the effect of considering the hypocentral depth as an additional variable for the attenuation model, using as the target the tendency of the average stress drop to increase with depth, as observed in recent studies. We analyze the Fourier spectra of S-wave windows for about 1900 earthquakes with a magnitude above 2.5 recorded in the Ridgecrest region, southern California. Two different parameterizations of the attenuation term are implemented in the spectral decomposition, either as a function of the hypocentral distance alone or as a function of both epicentral distance and depth. The comparison of the spectral attenuation curves shows that, although the hypocentral model describes, on average, the range of values spanned by the attenuation curve for different depths, systematic differences with distance, depth, and frequency are observed. These differences are transferred to the source spectra and, in turn, to the source parameters extracted from the best-fitting ω−2 models. In particular, stress drops for events deeper than 7 km are, on average, almost double even when depth is introduced explicitly in the attenuation model. The increase of stress drop with depth is confirmed also after accounting for the increase of the shear velocity with depth, which absorbs about 30%–40% of the total increase. Moreover, a qualitative comparison with a model for the gradient of the effective normal stress confirms the reliability of the observed trend. Finally, the coherent spatial patterns shown by a simplified 2D tomographic representation of the spectral residuals highlights the impact on ground-shaking variability of the lateral variability of the crustal attenuation properties in the region.

scholarly journals Notes regarding the Modeling of the Angle of Attack

2019 ◽  
Vol 304 ◽  
pp. 07012
Author(s):  
Laurentiu Moraru
Keyword(s):  
Numerical Integration ◽  
Equations Of Motion ◽  
Angle Of Attack ◽  
Numerical Algorithms ◽  
Simulated Data ◽  
Flight Simulation ◽  
Approximate Analytical Solutions ◽  
Long Time ◽  
Integration Algorithms ◽  
Nonlinear Equations Of Motion

Numerical integration has become routine for many decades and so has become the numerical integration of the aircraft’s equation of motion. Many numerical algorithms have been used in flight dynamics and the applications of the basic numerical methods to flight simulation have been included in textbooks for a long time. However, many design and/or optimization algorithms rely on analyzing large amounts of simulated data, so analytical algorithms that can provide expedite estimations of the fast varying parameters have been revaluated. The current paper discusses approximate analytical solutions for the angle of attack. Two types of such solutions are discussed. The first model considered originates in the classically linearized equations of motion. The second model discussed was obtained by simplifying the nonlinear equations of motion. The two models are compared against numerical results, provided by classical numerical integration algorithms.

Parallelizing the spectral transform method

1992 ◽  
Vol 4 (4) ◽  
pp. 269-291 ◽  
Author(s):  
Patrick H. Worley ◽  
John B. Drake
Keyword(s):  
Transform Method ◽  
Spectral Transform

scholarly journals NUMERICAL MODEL FOR AIR POLLUTION SIMULATION FROM ROAD TRANSPORT

2021 ◽  
Vol 1 (5(69)) ◽  
pp. 58-63
Author(s):  
M. Biliaiev ◽  
V. Biliaieva ◽  
O. Berlov ◽  
V. Kozachyna
Keyword(s):  
Air Pollution ◽  
Numerical Model ◽  
Finite Difference ◽  
Numerical Integration ◽  
Complex Terrain ◽  
Computer Code ◽  
Road Transport ◽  
Finite Difference Schemes ◽  
Air Pollution Modelling ◽  
Pollutant Transfer

The problem of air pollution modelling near road which is situated in complex terrain is under consideration. To simulate wind flow pattern in case of complex terrain Navier-Stokes’s equations were used. NavierStokes’s equations were written using Helmholtz variables. Numerical finite difference schemes of splitting were used for numerical integration of Navier-Stokes’s equations. Equation of connective-diffusive pollutant transfer was used to simulate air pollution. Finite difference scheme of splitting was used for numerical integration of convectivediffusive equation of pollutant transfer. Computer code was developed on the basis of created numerical model. The results of a numerical experiment are presented.

scholarly journals Applying splitting methods with complex coefficients to the numerical integration of unitary problems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Sergio Blanes ◽  
Fernando Casas ◽  
Alejandro Escorihuela-Tomàs
Keyword(s):  
Numerical Integration ◽  
Numerical Approximation ◽  
Splitting Methods ◽  
Time Dependent ◽  
Small Step ◽  
Time Intervals ◽  
Long Time ◽  
Complex Coefficients ◽  
Pseudo Spectral ◽  
Spectral Discretization

<p style='text-indent:20px;'>We explore the applicability of splitting methods involving complex coefficients to solve numerically the time-dependent Schrödinger equation. We prove that a particular class of integrators are conjugate to unitary methods for sufficiently small step sizes when applied to problems defined in the group <inline-formula><tex-math id="M1">\begin{document}$ \mathrm{SU}(2) $\end{document}</tex-math></inline-formula>. In the general case, the error in both the energy and the norm of the numerical approximation provided by these methods does not possess a secular component over long time intervals, when combined with pseudo-spectral discretization techniques in space.</p>

Sign in / Sign up

Export Citation Format

Share Document