41,785 research outputs found
Invariant Discretization Schemes Using Evolution-Projection Techniques
Finite difference discretization schemes preserving a subgroup of the maximal
Lie invariance group of the one-dimensional linear heat equation are
determined. These invariant schemes are constructed using the invariantization
procedure for non-invariant schemes of the heat equation in computational
coordinates. We propose a new methodology for handling moving discretization
grids which are generally indispensable for invariant numerical schemes. The
idea is to use the invariant grid equation, which determines the locations of
the grid point at the next time level only for a single integration step and
then to project the obtained solution to the regular grid using invariant
interpolation schemes. This guarantees that the scheme is invariant and allows
one to work on the simpler stationary grids. The discretization errors of the
invariant schemes are established and their convergence rates are estimated.
Numerical tests are carried out to shed some light on the numerical properties
of invariant discretization schemes using the proposed evolution-projection
strategy
Wavelet-based Adaptive Techniques Applied to Turbulent Hypersonic Scramjet Intake Flows
The simulation of hypersonic flows is computationally demanding due to large
gradients of the flow variables caused by strong shock waves and thick boundary
or shear layers. The resolution of those gradients imposes the use of extremely
small cells in the respective regions. Taking turbulence into account
intensives the variation in scales even more. Furthermore, hypersonic flows
have been shown to be extremely grid sensitive. For the simulation of
three-dimensional configurations of engineering applications, this results in a
huge amount of cells and prohibitive computational time. Therefore, modern
adaptive techniques can provide a gain with respect to computational costs and
accuracy, allowing the generation of locally highly resolved flow regions where
they are needed and retaining an otherwise smooth distribution. An h-adaptive
technique based on wavelets is employed for the solution of hypersonic flows.
The compressible Reynolds averaged Navier-Stokes equations are solved using a
differential Reynolds stress turbulence model, well suited to predict
shock-wave-boundary-layer interactions in high enthalpy flows. Two test cases
are considered: a compression corner and a scramjet intake. The compression
corner is a classical test case in hypersonic flow investigations because it
poses a shock-wave-turbulent-boundary-layer interaction problem. The adaptive
procedure is applied to a two-dimensional confguration as validation. The
scramjet intake is firstly computed in two dimensions. Subsequently a
three-dimensional geometry is considered. Both test cases are validated with
experimental data and compared to non-adaptive computations. The results show
that the use of an adaptive technique for hypersonic turbulent flows at high
enthalpy conditions can strongly improve the performance in terms of memory and
CPU time while at the same time maintaining the required accuracy of the
results.Comment: 26 pages, 29 Figures, submitted to AIAA Journa
Interplay of spatial dynamics and local adaptation shapes species lifetime distributions and species-area relationships
The distributions of species lifetimes and species in space are related,
since species with good local survival chances have more time to colonize new
habitats and species inhabiting large areas have higher chances to survive
local disturbances. Yet, both distributions have been discussed in mostly
separate communities. Here, we study both patterns simultaneously using a
spatially explicit, evolutionary community assembly approach. We present and
investigate a metacommunity model, consisting of a grid of patches, where each
patch contains a local food web. Species survival depends on predation and
competition interactions, which in turn depend on species body masses as the
key traits. The system evolves due to the migration of species to neighboring
patches, the addition of new species as modifications of existing species, and
local extinction events. The structure of each local food web thus emerges in a
self-organized manner as the highly non-trivial outcome of the relative time
scales of these processes. Our model generates a large variety of complex,
multi-trophic networks and therefore serves as a powerful tool to investigate
ecosystems on long temporal and large spatial scales. We find that the observed
lifetime distributions and species-area relations resemble power laws over
appropriately chosen parameter ranges and thus agree qualitatively with
empirical findings. Moreover, we observe strong finite-size effects, and a
dependence of the relationships on the trophic level of the species. By
comparing our results to simple neutral models found in the literature, we
identify the features that are responsible for the values of the exponents.Comment: Theor Ecol (2019
The DUNE-ALUGrid Module
In this paper we present the new DUNE-ALUGrid module. This module contains a
major overhaul of the sources from the ALUgrid library and the binding to the
DUNE software framework. The main changes include user defined load balancing,
parallel grid construction, and an redesign of the 2d grid which can now also
be used for parallel computations. In addition many improvements have been
introduced into the code to increase the parallel efficiency and to decrease
the memory footprint.
The original ALUGrid library is widely used within the DUNE community due to
its good parallel performance for problems requiring local adaptivity and
dynamic load balancing. Therefore, this new model will benefit a number of DUNE
users. In addition we have added features to increase the range of problems for
which the grid manager can be used, for example, introducing a 3d tetrahedral
grid using a parallel newest vertex bisection algorithm for conforming grid
refinement. In this paper we will discuss the new features, extensions to the
DUNE interface, and explain for various examples how the code is used in
parallel environments.Comment: 25 pages, 11 figure
- …