Propagation of diffusing pollutant by kinetic flux-vector splitting method
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Saqib Zia
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Omar Rabbani
Abstract
In this article, the transport of a passive pollutant by a flow modeled by shallow water equations is numerically investigated. The kinetic flux-vector splitting (KFVS) scheme is extended to solve the one and two-dimensional equations. The first two equations of the considered model are mass and momentum equations and the third equation is the transport equation. The suggested scheme focuses on the direct splitting of the macroscopic flux functions at the cell interfaces. It achieves second-order accuracy by using MUSCL-type initial reconstruction and the Runge–Kutta time stepping technique. Several numerical test problems from literature are considered to check the efficiency and performance of the scheme. The results of the proposed scheme are compared to the central scheme for validation. It is found that the results of both the schemes are in close agreement with each other. However, our suggested KFVS scheme resolves the sharp discontinuous profiles precisely.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Dynamics of synthetic drug transmission models
- Collision-induced amplitude dynamics of pulses in linear waveguides with the generic nonlinear loss
- Global dissipativity of non-autonomous BAM neural networks with mixed time-varying delays and discontinuous activations
- On the inverse problem for nonlinear strongly damped wave equations with discrete random noise
- A second-order nonlocal regularized variational model for multiframe image super-resolution
- Algebro-geometric integration of a modified shallow wave hierarchy
- Singularity analysis of a 7-DOF spatial hybrid manipulator for medical surgery
- Propagation of diffusing pollutant by kinetic flux-vector splitting method
- Limit cycles in a tritrophic food chain model with general functional responses
- Local and parallel stabilized finite element methods based on full domain decomposition for the stationary Stokes equations
- Stress concentration effect on deflection and stress fields of a master leaf spring through domain decomposition and geometry updation technique
- Electrostatically actuated double walled piezoelectric nanoshell subjected to nonlinear van der Waals effect: nonclassical vibrations and stability analysis
- Traveling wave solutions of the generalized Rosenau–Kawahara-RLW equation via the sine–cosine method and a generalized auxiliary equation method
- A predictor–corrector compact finite difference scheme for a nonlinear partial integro-differential equation
- Parameter inference with analytical propagators for stochastic models of autoregulated gene expression
- DCSK performance analysis of a chaos-based communication using a newly designed chaotic system
- On successive linearization method for differential equations with nonlinear conditions
- Comparison of different time discretization schemes for solving the Allen–Cahn equation
- The homoclinic breather wave solution, rational wave and n-soliton solution to a nonlinear differential equation
- Diversity of interaction phenomenon, cross-kink wave, and the bright-dark solitons for the (3 + 1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like equation
