# Methods of Calculation of Hazardous and Contaminating Substance Spread over the Terrain Surface

Annotation:

The study considers and compares several methods of calculation of the process of stable liquid spread over a solid impermeable surface: the SPH method and the VOF method for the three-dimensional system of equations; the Lax-Wendroff method and the finite volume method for the two-dimensional «shallow water» system of equations. The «shallow water» systems of equations are obtained by averaging the full system of equations over depth assuming the absence of a vertical velocity component. The procedure of numerical calculation by the Lax-Wendroff method is provided in detail.
The emphasis is made on considering shallow water approximation as such approximation enables obtaining a three-dimensional flow pattern in the framework of a two-dimensional model. The «shallow water» system of equations is provided taking into account the action of friction forces.
All four calculation methods have been verified by using the data of a water dam breaking experiment in a 122-meter canal. The experiments recorded the dynamics of liquid propagation and water rise at different locations and moments.
The comparison implies that the SPH method requires significant computational costs due to the need to specify a large number of particles in order to ensure acceptable accuracy. The VOF calculation method blurs the air-water interface, which hampers the determination of spill configuration and the free surface position. The dam breaking problem has been solved most accurately by two methods, namely the Lax-Wendroff method and the finite volume method, which has been confirmed by the quantitative assessment of error in calculations by various methods.
It has been demonstrated that the shallow water approximation implemented by the Lax-Wendroff numerical method used in the study ensures accuracy sufficient to solve problems of spill over the terrain surface.

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DOI: 10.24000/0409-2961-2024-2-16-23
Year: 2024
Issue num: February
Keywords : загрязняющие вещества calculation methods liquid spill on the terrain SPH method Lax-Wendroff method the «volume of fluid» method «shallow water» equations dynamic pattern of a spill
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