6,129 research outputs found
TSIL: a program for the calculation of two-loop self-energy integrals
TSIL is a library of utilities for the numerical calculation of dimensionally
regularized two-loop self-energy integrals. A convenient basis for these
functions is given by the integrals obtained at the end of O.V. Tarasov's
recurrence relation algorithm. The program computes the values of all of these
basis functions, for arbitrary input masses and external momentum. When
analytical expressions in terms of polylogarithms are available, they are used.
Otherwise, the evaluation proceeds by a Runge-Kutta integration of the coupled
first-order differential equations for the basis integrals, using the external
momentum invariant as the independent variable. The starting point of the
integration is provided by known analytic expressions at (or near) zero
external momentum. The code is written in C, and may be linked from C, C++, or
Fortran. A Fortran interface is provided. We describe the structure and usage
of the program, and provide a simple example application. We also compute two
new cases analytically, and compare all of our notations and conventions for
the two-loop self-energy integrals to those used by several other groups.Comment: 31 pages. Updated to reflect new functionality through v1.4 May 2016
and new information about use with C++. Source code and documentation are
available at http://www.niu.edu/spmartin/TSIL or
http://faculty.otterbein.edu/DRobertson/tsil
More efficient time integration for Fourier pseudo-spectral DNS of incompressible turbulence
Time integration of Fourier pseudo-spectral DNS is usually performed using
the classical fourth-order accurate Runge--Kutta method, or other methods of
second or third order, with a fixed step size. We investigate the use of
higher-order Runge-Kutta pairs and automatic step size control based on local
error estimation. We find that the fifth-order accurate Runge--Kutta pair of
Bogacki \& Shampine gives much greater accuracy at a significantly reduced
computational cost. Specifically, we demonstrate speedups of 2x-10x for the
same accuracy. Numerical tests (including the Taylor-Green vortex,
Rayleigh-Taylor instability, and homogeneous isotropic turbulence) confirm the
reliability and efficiency of the method. We also show that adaptive time
stepping provides a significant computational advantage for some problems (like
the development of a Rayleigh-Taylor instability) without compromising
accuracy
General relativistic null-cone evolutions with a high-order scheme
We present a high-order scheme for solving the full non-linear Einstein
equations on characteristic null hypersurfaces using the framework established
by Bondi and Sachs. This formalism allows asymptotically flat spaces to be
represented on a finite, compactified grid, and is thus ideal for far-field
studies of gravitational radiation. We have designed an algorithm based on
4th-order radial integration and finite differencing, and a spectral
representation of angular components. The scheme can offer significantly more
accuracy with relatively low computational cost compared to previous methods as
a result of the higher-order discretization. Based on a newly implemented code,
we show that the new numerical scheme remains stable and is convergent at the
expected order of accuracy.Comment: 24 pages, 3 figure
Two-dimensional Euler and Navier-Stokes Time accurate simulations of fan rotor flows
Two numerical methods are presented which describe the unsteady flow field in the blade-to-blade plane of an axial fan rotor. These methods solve the compressible, time-dependent, Euler and the compressible, turbulent, time-dependent, Navier-Stokes conservation equations for mass, momentum, and energy. The Navier-Stokes equations are written in Favre-averaged form and are closed with an approximate two-equation turbulence model with low Reynolds number and compressibility effects included. The unsteady aerodynamic component is obtained by superposing inflow or outflow unsteadiness to the steady conditions through time-dependent boundary conditions. The integration in space is performed by using a finite volume scheme, and the integration in time is performed by using k-stage Runge-Kutta schemes, k = 2,5. The numerical integration algorithm allows the reduction of the computational cost of an unsteady simulation involving high frequency disturbances in both CPU time and memory requirements. Less than 200 sec of CPU time are required to advance the Euler equations in a computational grid made up of about 2000 grid during 10,000 time steps on a CRAY Y-MP computer, with a required memory of less than 0.3 megawords
Space-time discontinuous Galerkin finite element method for shallow water flows
A space-time discontinuous Galerkin (DG) finite element method is presented for the shallow water equations over varying bottom topography. The method results in non-linear equations per element, which are solved locally by establishing the element communication with a numerical HLLC flux. To deal with spurious oscillations around discontinuities, we employ a dissipation operator only around discontinuities using Krivodonova's discontinuity detector. The numerical scheme is verified by comparing numerical and exact solutions, and validated against a laboratory experiment involving flow through a contraction. We conclude that the method is second order accurate in both space and time for linear polynomials.\u
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