Integral sentences and numerical comparative calculations for the validity of the dispersion model for air pollutants AUSTAL2000
Authors: Rainer Schenk 
Published: August 2020

Abstract
*Background: The authors Janicke (Janicke U, Janicke L (2002). Development of a model-based assessment system for machine-related immission control. IB Janicke Dunum) developed an expansion model under the name AUSTAL2000. This becomes effective in the Federal Republic of Germany with the entry into force of TA Luft (BMU (2002) First general administrative regulation for the Federal Immission Control Act (technical instructions for keeping air TA air clean) from July 24, 2002. GMBL issue 25-29 S: 511-605 ) declared binding in 2002. Immediately after publication, the first doubts about the validity of the reference solutions are raised in individual cases. The author of this article, for example, is asked by senior employees of the immission control to express their opinions. However, questions regarding clarification in the engineering office Janicke in Dunum remain unanswered. In 2014, the author of this article was again questioned by interested environmental engineers about the validity of the reference solutions of the AUSTAL dispersion model. In the course of a clarification, the company WESTKAL, United Warstein Limestone Industry, later placed an order to develop expertise on this model development, Schenk (Schenk R. (2014) Expertise on Austal 2000. Report on behalf of the United Warstein Limestone Industry, Westkalk Archives and IBS). The results of this expertise form the background of all publications on the criticism of Schenk's AUSTAL expansion model. It is found that all reference solutions violate all main and conservation laws. Peculiar terms used spread confusion rather than enlightenment. For example, one confuses process engineering homogenization with diffusion. When homogenizing, one notices strange vibrations at the range limits, which cannot be explained further. It remains uncertain whether this is due to numerical instabilities. However, it is itself stated that in some cases the solutions cannot converge. The simulations should then be repeated with different input parameters. Concentrations are calculated inside AUSTAL. In this context, it is noteworthy that no publication by the AUSTAL authors specifies functional analysis, e.g. for stability, convergence and consistency. Concentrations are calculated inside closed buildings. It is explained that dust particles cannot “see” vertical walls and therefore want to pass through them. One calculates with “volume sources over the entire computing area”. However, such sources are unknown in the theory of modeling the spread of air pollutants. Deposition speeds are defined at will. 3D wind fields should be used for validation. The rigid rotation of a solid in the plane is actually used. Diffusion tensors are formulated without demonstrating that their coordinates have to comply with the laws of transformation and cannot be chosen arbitrarily. Constant concentration distributions only occur when there are no “external forces”. It is obviously not known that the relevant model equations are mass balances and not force equations. AUSTAL also claims to be able to perform non-stationary simulations. One pretends to have calculated time series. However, it is not possible to find out in all reports which time-dependent analytical solution the algorithm could have been validated with. A three-dimensional control room is described, but only zero and one-dimensional solutions are given. All reference examples with "volume source distributed over the entire computing area" turn out to be useless trivial cases. The AUSTAL authors believe that “a linear combination of two wind fields results in a valid wind field”. Obviously, one does not know that wind fields are only described by second-degree momentum equations, which excludes any linear combinations. It is claimed that Berljand profiles have been recalculated. In fact, one doesn't care about three-dimensional concentration distributions. On the one hand, non-stationary tasks are described, but only stationary solutions are discussed. In another reference, non-stationary solutions are explained in reverse, but only stationary model equations are considered. Further contradictions can be found in the original literature by the AUSTAL authors. The public is misled. The aim of the present work is to untangle the absent-mindedness of the AUSTAL authors by means of mathematics and mechanics, to collect, to order and to systematize the information. This specifies the relevant tasks for the derivation of stationary and non-stationary reference solutions. They can be compared to the solutions of the AUSTAL authors. These results should make it possible to make clear conclusions about the validity of the AUSTAL model.*Results: Using the example of deriving reference solutions for spreading, sedimentation and deposition, the author of this work describes the necessary mathematical and physical principles. This includes the differential equations for stationary and non-stationary tasks as well as the relevant initial and boundary conditions. The valid initial boundary value task is explained. The correct solutions are given and compared to the wrong algorithms of the AUSTAL authors. In order to check the validity of the main and conservation laws, integral equations are developed, which are subsequently applied to all solutions. Numerical comparative calculations are used to check non-stationary solutions, for which an algorithm is independently developed. The analogy to the impulse, heat and mass transport is also used to analyze the reference solutions of the AUSTAL authors. If one follows this analogy, all reference solutions by the AUSTAL authors comparatively violate Newton’s 3rd axiom. As a result, the author of this article comes to the conclusion that all reference solutions by the AUSTAL authors violate the mass conservation law. Earlier statements on this are confirmed and substantiated further. All applications with "volume source distributed over the entire computing area" turn out to be useless zero-dimensional trivial cases. The information provided by the AUSTAL authors on non-stationary solutions has not been documented throughout. The authors of AUSTAL have readers puzzled about why, for example, the stationary solution should have set in after 10 days for each reference case. It turns out that no non-stationary calculations could be carried out at all. In order to gain in-depth knowledge of the development of AUSTAL, the author of this article deals with his life story. It begins according to Axenfeld et al. (Axenfeld F, Janicke L, Münch J (1984) Development of a model for the calculation of dust precipitation. Environmental research plan of the Federal Minister of the Interior for Air Pollution Control, research report 104 02 562, Dornier System GmbH Friedrichshafen, on behalf of the Federal Environment Agency), according to which one is under deposition loss and not Storage understands. In the end, the AUSTAL authors take refuge in Trukenmüller (Trukenmüller A (2016) equivalence of the reference solutions from Schenk and Janicke. Treatise Umweltbundesamt Dessau-Rosslau S: 1 - 5) in incomprehensible evidence. How Trukenmüller gets more and more involved in contradictions can be found in (Trukenmüller A (2017) Treatises of the Federal Environment Agency from February 10th, 2017 and March 23rd, 2017. Dessau-Rosslau S: 1-15).*Conclusion: The author of this article comes to the conclusion that the dispersion model for air pollutants AUSTAL is not validated. Dispersion calculations for sedimentation and depositions cannot be carried out with this model. The authors of AUSTAL have to demonstrate how one can recalculate nature experiments with a dispersion model that contradicts all valid principles. Applications important for health and safety, e.g. Security analyzes, hazard prevention plans and immission forecasts are to be checked with physically based model developments. Court decisions are also affected.