scholarly journals A consistent implementation of point sources on finite-difference grids

2020 ◽  
Vol 223 (2) ◽  
pp. 1144-1161
Author(s):  
Erik F M Koene ◽  
Johan O A Robertsson ◽  
Fredrik Andersson
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Point Source ◽  
Point Sources ◽  
Sinc Function ◽  
Machine Precision ◽  
Single Node ◽  
Distributed Source ◽  
Spatial Point ◽  
Spatially Distributed

SUMMARY We present a method to position point sources at arbitrary locations on finite-difference (FD) grids. We show that implementing point sources on single nodes can cause considerable errors when modelling with the FD method. In contrast, we propose to create a spatially distributed source (over multiple nodes) that nonetheless creates the desired point-source response. The spatial point source is formulated in the wavenumber domain and is based on the FD coefficients used for the wave propagation. Using this ‘FD-consistent source’ on 1-D and 2-D examples, we show that we can obtain superior fits to analytical solutions compared to single-node or sinc-function source implementations, and we show that sources can be offset to arbitrary locations from ‘on’ the grid to ‘off’ the grid, while resulting in solutions that are identical to within machine precision

scholarly journals Anisotropic elastic finite-difference modeling of sources and receivers on Lebedev grids

Geophysics ◽  
2020 ◽  
pp. 1-19
Author(s):  
Erik F.M. Koene ◽  
Johan O.A. Robertsson ◽  
Fredrik Andersson
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Point Source ◽  
Point Sources ◽  
Elastic Wave Propagation ◽  
Novel Approach ◽  
Distributed Array ◽  
Anisotropic Elastic

The Lebedev grid finite-difference (FD) method allows modeling of anisotropic elastic wave propagation. On Lebedev grids, erroneous point-source excitations can create spurious (non-physical) waves. The only known remedy for such artifacts in the literature is the Lisitsa-Vishnevsky method. This method uses a distributed array to create both point-sources and point-receivers on the FD grid. However, the Lisitsa-Vishnevsky method does not fully eliminate spurious artifacts. A novel approach is found in the FD-consistent point-source, which suppresses the spurious artifacts entirely. The method requires no array recording to create point-receivers. The advantage of this method over the Lisitsa-Vishnevsky method is demonstrated with two anisotropic modeling examples.

A Conceptual Model for Cryptosporidium Transport in Watersheds

2003 ◽  
Vol 38 (1) ◽  
pp. 77-113 ◽  
Author(s):  
Chan Hee Park ◽  
Peter M. Huck
Keyword(s):  
Water Treatment ◽  
Finite Difference ◽  
Point Source ◽  
Conceptual Model ◽  
Treatment Plant ◽  
Water Treatment Plant ◽  
Point Sources ◽  
Experimental Investigations ◽  
Base Case ◽  
Data Set

Abstract This paper describes a conceptual model to estimate Cryptosporidium parvum oocyst transport from source to water treatment plant intake. The intent of the model is ultimately to be able to predict oocyst concentrations at an intake to an order-of-magnitude level. The transport and fate mechanisms included are: oocyst detachment from waste or soil, generation of runoff, overland transport, reservoir and in-stream transport, and oocyst die-off. The model is formulated in finite difference form, and deals with both non-point sources from manure-applied areas, and point sources from wastewater treatment plants. An important contribution of this work is the recognition that the settling rates of free and floc- or particle-associated oocysts can be considerably different. This has important implications for their transport. A finite difference scheme was developed for five sections of a hypothetical watershed: a point source, a lake or reservoir (which can be modelled as either a continuous stirred tank reactor or an ideal rectangular setting tank), the section of stream channel from the outlet of the lake or reservoir to the confluence with another stream, a tributary with a non-point source, and the stream section from the confluence to a water treatment plant intake. The stream confluence is handled with a simple mass and flow balance. It would be very expensive to collect the necessary data to test the model. Because an appropriate data set was not available, the model was tested by means of a sensitivity analysis for the hypothetical watershed, using reasonable parameter settings for the base case. The major contribution of the model is in defining the mechanisms involved in oocyst transport within a watershed. It gives important insights into the significance of various factors, provides a basis for data collection, and identifies areas where experimental investigations are required to avoid the need for simplifying assumptions. At its current state of development, the model cannot be used to provide quantitative predictions, but defines a base from which further detailed modelling can be developed to aid in decisionmaking for pathogen control. Using the framework that this model provides, contributions from other sources of Cryptosporidium oocysts such as domestic animals and combined sewage overflows could also be modelled.

Finite‐difference modeling of scalar‐wave propagation in cracked media

Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 267-276 ◽  
Author(s):  
Gerben B. van Baren ◽  
Wim A. Mulder ◽  
Gérard C. Herman
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Point Sources ◽  
Small Scale ◽  
Scalar Wave ◽  
Equation Solution ◽  
Finite Difference Technique ◽  
Embedding Medium

We discuss a finite‐difference modeling technique for the simplified case of scalar, two‐dimensional wave propagation in a medium containing a large number of small‐scale cracks. The cracks are characterized by an explicit (Neumann) boundary condition whereas the embedding medium can be heterogeneous. The boundaries of the cracks are not represented in the finite‐difference mesh, but the cracks are incorporated as distributed point sources. This enables the use of grid cells that are considerably larger than the crack sizes. We compare our method to an accurate integral‐equation solution for the case of a homogeneous embedding and conclude that the finite‐difference technique is accurate and computationally fast.

FINITE-DIFFERENCE MODELING IN MEDIA WITH MANY SMALL-SCALE CRACKS

2001 ◽  
Vol 09 (03) ◽  
pp. 815-831
Author(s):  
GERBEN B. VAN BAREN ◽  
GERARD C. HERMAN ◽  
WIM A. MULDER
Keyword(s):  
Integral Equation ◽  
Wave Propagation ◽  
Finite Difference ◽  
Point Sources ◽  
Small Scale ◽  
Two Dimensional ◽  
Equation Solution ◽  
Finite Difference Technique ◽  
Embedding Medium ◽  
Dimensional Wave

We discuss a finite-difference modeling technique for scalar, two-dimensional wave propagation in a medium containing a large number of small-scale cracks. The embedding medium can be heterogeneous. The boundaries of the cracks are not represented in the finite-difference mesh but the cracks are incorporated as distributed point sources. This enables the use of grid cells that are considerably larger than the crack sizes. We compare our method to an accurate integral-equation solution for the case of a homogeneous embedding and conclude that the finite-difference technique is accurate and computationally fast.

Sources of Nitrogen and Phosphorus in the Catchment Area of Neusiedlersee/Fertö, Austria/Hungary

1993 ◽  
Vol 28 (3-5) ◽  
pp. 101-110 ◽  
Author(s):  
W. v. d. Emde ◽  
H. Fleckseder ◽  
N. Matsché ◽  
F. Plahl-Wabnegg ◽  
G. Spatzierer ◽  
...  
Keyword(s):  
Point Source ◽  
Catchment Area ◽  
Management Practice ◽  
Water Erosion ◽  
Nonpoint Source ◽  
Point Sources ◽  
Source Control ◽  
Nitrogen And Phosphorus ◽  
Catchment Areas ◽  
The One

Neusiedlersee (in German) / Fertö tó (in Hungarian) is a shallow lake at the Austro-Hungarian border. In the late 1970s, the question arose what to do in order to protect the lake against eutrophication. A preliminary report established the need for point-source control as well as gave first estimates for non-point source inputs. The proposed point-source control was quickly implemented, non-point sources were - among other topics - studied in detail in the period 1982 - 1986. The preliminary work had shown, based on integrated sampling and data from literature, that the aeolic input outweighed the one via water erosion (work was for totP only). In contrast to this, the 1982 - 1986 study showed that (a) water erosion by far dominates over aeolic inputs and (b) the size of nonpoint-source inputs was assessed for the largest catchment area in pronounced detail, whereas additional estimates were undertaken for smaller additional catchment areas. The methods as well as the results are presented in the following. The paper concludes with some remarks on the present management practice of nonpoint-source inputs.

Incorporation of spatial variability in modeling non-point source groundwater nitrate pollution

1996 ◽  
Vol 33 (4-5) ◽  
pp. 233-240 ◽  
Author(s):  
F. S. Goderya ◽  
M. F. Dahab ◽  
W. E. Woldt ◽  
I. Bogardi
Keyword(s):  
Spatial Variability ◽  
Point Source ◽  
Three Dimensional ◽  
Nitrate Contamination ◽  
Geostatistical Simulation ◽  
Chemical Measurements ◽  
Spatially Distributed ◽  
Potential Benefits ◽  
Zone Modeling ◽  
Physical And Chemical

A methodology for incorporation of spatial variability in modeling non-point source groundwater nitrate contamination is presented. The methodology combines geostatistical simulation and unsaturated zone modeling for estimating the amount of nitrate loading to groundwater. Three dimensional soil nitrogen variability and 2-dimensional crop yield variability are used in quantifying potential benefits of spatially distributed nitrogen input. This technique, in combination with physical and chemical measurements, is utilized as a means of illustrating how the spatial statistical properties of nitrate leaching can be obtained for different scenarios of fixed and variable rate nitrogen applications.

scholarly journals TNO-MACC_II emission inventory; a multi-year (2003–2009) consistent high-resolution European emission inventory for air quality modelling

2014 ◽  
Vol 14 (20) ◽  
pp. 10963-10976 ◽  
Author(s):  
J. J. P. Kuenen ◽  
A. J. H. Visschedijk ◽  
M. Jozwicka ◽  
H. A. C. Denier van der Gon
Keyword(s):  
Particulate Matter ◽  
Air Quality ◽  
High Resolution ◽  
Emission Inventory ◽  
Point Sources ◽  
Air Quality Modelling ◽  
Emission Data ◽  
Data Set ◽  
Spatially Distributed ◽  
Reported Data

Abstract. Emissions to air are reported by countries to EMEP. The emissions data are used for country compliance checking with EU emission ceilings and associated emission reductions. The emissions data are also necessary as input for air quality modelling. The quality of these "official" emissions varies across Europe. As alternative to these official emissions, a spatially explicit high-resolution emission inventory (7 × 7 km) for UNECE-Europe for all years between 2003 and 2009 for the main air pollutants was made. The primary goal was to supply air quality modellers with the input they need. The inventory was constructed by using the reported emission national totals by sector where the quality is sufficient. The reported data were analysed by sector in detail, and completed with alternative emission estimates as needed. This resulted in a complete emission inventory for all countries. For particulate matter, for each source emissions have been split in coarse and fine particulate matter, and further disaggregated to EC, OC, SO4, Na and other minerals using fractions based on the literature. Doing this at the most detailed sectoral level in the database implies that a consistent set was obtained across Europe. This allows better comparisons with observational data which can, through feedback, help to further identify uncertain sources and/or support emission inventory improvements for this highly uncertain pollutant. The resulting emission data set was spatially distributed consistently across all countries by using proxy parameters. Point sources were spatially distributed using the specific location of the point source. The spatial distribution for the point sources was made year-specific. The TNO-MACC_II is an update of the TNO-MACC emission data set. Major updates included the time extension towards 2009, use of the latest available reported data (including updates and corrections made until early 2012) and updates in distribution maps.

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