3,945 research outputs found
Two dimensional sediment transport model using parallel computers
Management and development of water bodies is vital for meeting domestic, agricultural, energy and industrial needs. To that end, dams, artificial channels, lakes and other water structures have been constructed. Management and development of these structures encounter problems of land erosion, reservoir silting, and degradation and aggradation of channel beds, which need to be addressed. Fundamental to these problems are sediment transport, erosion and deposition. Numerical modeling of sediment transport is the best tool to simulate sediment transport in a water body. This study develops a vertically integrated two-dimensional numerical sediment transport model. Sediment transport is simulated in two parts in this model: suspended load and bed load. A fractional step approach is used to solve the two-dimensional advection diffusion equation, which splits the advection-diffusion equation in to two separate parts: advection and diffusion. High resolution conservative algorithm is used to solve the advection part and a semi implicit finite difference scheme is used to solve the diffusion part. Different parallel numerical solvers are developed to solve linear system of equations resulting from diffusion part. Non-uniformity in sediment mixture which is quite common in real world problems is considered. The model is tested for different analytical and laboratory test cases. The model is coded for parallel computers so that enormous power of parallel computers can be exploited
Positive approximations of the inverse of fractional powers of SPD M-matrices
This study is motivated by the recent development in the fractional calculus
and its applications. During last few years, several different techniques are
proposed to localize the nonlocal fractional diffusion operator. They are based
on transformation of the original problem to a local elliptic or
pseudoparabolic problem, or to an integral representation of the solution, thus
increasing the dimension of the computational domain. More recently, an
alternative approach aimed at reducing the computational complexity was
developed. The linear algebraic system , is considered, where is a properly normalized (scalded) symmetric
and positive definite matrix obtained from finite element or finite difference
approximation of second order elliptic problems in ,
. The method is based on best uniform rational approximations (BURA)
of the function for and natural .
The maximum principles are among the major qualitative properties of linear
elliptic operators/PDEs. In many studies and applications, it is important that
such properties are preserved by the selected numerical solution method. In
this paper we present and analyze the properties of positive approximations of
obtained by the BURA technique. Sufficient conditions for
positiveness are proven, complemented by sharp error estimates. The theoretical
results are supported by representative numerical tests
The LifeV library: engineering mathematics beyond the proof of concept
LifeV is a library for the finite element (FE) solution of partial
differential equations in one, two, and three dimensions. It is written in C++
and designed to run on diverse parallel architectures, including cloud and high
performance computing facilities. In spite of its academic research nature,
meaning a library for the development and testing of new methods, one
distinguishing feature of LifeV is its use on real world problems and it is
intended to provide a tool for many engineering applications. It has been
actually used in computational hemodynamics, including cardiac mechanics and
fluid-structure interaction problems, in porous media, ice sheets dynamics for
both forward and inverse problems. In this paper we give a short overview of
the features of LifeV and its coding paradigms on simple problems. The main
focus is on the parallel environment which is mainly driven by domain
decomposition methods and based on external libraries such as MPI, the Trilinos
project, HDF5 and ParMetis.
Dedicated to the memory of Fausto Saleri.Comment: Review of the LifeV Finite Element librar
A Second Order Godunov Method for Multidimensional Relativistic Magnetohydrodynamics
We describe a new Godunov algorithm for relativistic magnetohydrodynamics
(RMHD) that combines a simple, unsplit second order accurate integrator with
the constrained transport (CT) method for enforcing the solenoidal constraint
on the magnetic field. A variety of approximate Riemann solvers are implemented
to compute the fluxes of the conserved variables. The methods are tested with a
comprehensive suite of multidimensional problems. These tests have helped us
develop a hierarchy of correction steps that are applied when the integration
algorithm predicts unphysical states due to errors in the fluxes, or errors in
the inversion between conserved and primitive variables. Although used
exceedingly rarely, these corrections dramatically improve the stability of the
algorithm. We present preliminary results from the application of these
algorithms to two problems in RMHD: the propagation of supersonic magnetized
jets, and the amplification of magnetic field by turbulence driven by the
relativistic Kelvin-Helmholtz instability (KHI). Both of these applications
reveal important differences between the results computed with Riemann solvers
that adopt different approximations for the fluxes. For example, we show that
use of Riemann solvers which include both contact and rotational
discontinuities can increase the strength of the magnetic field within the
cocoon by a factor of ten in simulations of RMHD jets, and can increase the
spectral resolution of three-dimensional RMHD turbulence driven by the KHI by a
factor of 2. This increase in accuracy far outweighs the associated increase in
computational cost. Our RMHD scheme is publicly available as part of the Athena
code.Comment: 75 pages, 28 figures, accepted for publication in ApJS. Version with
high resolution figures available from
http://jila.colorado.edu/~krb3u/Athena_SR/rmhd_method_paper.pd
Computational studies of non-viscous and viscous fluid flows
This Bachelor’s Degree Thesis consists on a computational study of non-viscous andviscous fluid flows interacting with different external conditions and solid objects.The governing equations of fluid dynamics are Navier-Stokes equations. NS equa-tions are differentiate partial equations that are transformed into numerical expres-sions that can be computed.Simulations with the computer are runned for different reference cases for which aprevious solution has been obtained analytically or by researchers, beforehand.The principles, solvers and methods used to achieve a solution for the simulationscan be extrapolated to more complex problems
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