Mathematical Modeling and Numerical Simulation in Fluids

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 31 August 2024 | Viewed by 682

Special Issue Editor


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Guest Editor
National Center for Computational Hydroscience and Engineering, University of Mississippi, Oxford, MS 38655, USA
Interests: numerical model developments (1D, 2D, and 3D) and applications (flow simulation and sediment transport); mesh generations (1D channel networks; 2D structured and unstructured meshes); parallel computing; graphical users interface (GUI) development

Special Issue Information

Dear Colleagues,

Fluid-flow is dealing with motions of a fluid under unbalanced forces (fluid dynamics) and it typically associates with the transport phenomena (mass transfers, momentum transfers, and energy transfers). Understanding fluid-flows and the associated physical processes are important in many disciplines, including aerodynamics, hydraulics/hydrodynamics, and chemical/environmental engineering, etc. In addition to experimental and survey studies, with the advancement of computational technology, mathematical/numerical models have become powerful tools to study fluid flows and the associated processes.

This Special Issue is devoted to mathematical and computational investigations of fluid flows with associated physical processes. This issue contains articles on the developments, advancements, and applications of mathematical models, numerical methods/schemes, numerical analysis, techniques, and algorithms in a wide spectrum of fluid-flows-related processes. It should serve as a convenient forum for discussing trends and achievements, finding new solutions, and strengthening research collaborations and will be of interest to a wide range of specialists in fluids mechanics, hydraulics/hydrodynamics, coastal engineering, sediment transport, and environmental science.

This Special Issue will publish papers that present original and significant contributions on, but not limited to, the following potential topics:

  • Computational fluid dynamics;
  • Coastal modeling;
  • Chemical and pollutant transport;
  • Dam-break and flooding flows;
  • Flows in porous media;
  • Flows with complex boundary conditions;
  • Fluid–structure interactions;
  • Free surface flows;
  • Geological flows;
  • High performance computing;
  • Mathematics of fluids;
  • Multiphase flows;
  • Sediment transport and morphological changes;
  • Subsurface flows;
  • Turbulent flows;
  • Viscous and non-Newtonian flows.
  • Water quality modeling and evaluation;

This Special Issue aims at the demonstration of the powers of mathematical/numerical models in studying fluid flows and the associated processes. Full-length manuscripts in the aforementioned research directions are welcome.

Dr. Yaoxin Zhang
Guest Editor

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Keywords

  • fluid flows
  • numerical/mathematical models
  • numerical simulations
  • transport

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Published Papers (1 paper)

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Research

37 pages, 9513 KiB  
Article
Parallel Implicit Solvers for 2D Numerical Models on Structured Meshes
by Yaoxin Zhang, Mohammad Z. Al-Hamdan and Xiaobo Chao
Mathematics 2024, 12(14), 2184; https://doi.org/10.3390/math12142184 - 12 Jul 2024
Viewed by 376
Abstract
This paper presents the parallelization of two widely used implicit numerical solvers for the solution of partial differential equations on structured meshes, namely, the ADI (Alternating-Direction Implicit) solver for tridiagonal linear systems and the SIP (Strongly Implicit Procedure) solver for the penta-diagonal systems. [...] Read more.
This paper presents the parallelization of two widely used implicit numerical solvers for the solution of partial differential equations on structured meshes, namely, the ADI (Alternating-Direction Implicit) solver for tridiagonal linear systems and the SIP (Strongly Implicit Procedure) solver for the penta-diagonal systems. Both solvers were parallelized using CUDA (Computer Unified Device Architecture) Fortran on GPGPUs (General-Purpose Graphics Processing Units). The parallel ADI solver (P-ADI) is based on the Parallel Cyclic Reduction (PCR) algorithm, while the parallel SIP solver (P-SIP) uses the wave front method (WF) following a diagonal line calculation strategy. To map the solution schemes onto the hierarchical block-threads framework of the CUDA on the GPU, the P-ADI solver adopted two mapping methods, one block thread with iterations (OBM-it) and multi-block threads (MBMs), while the P-SIP solver also used two mappings, one conventional mapping using effective WF lines (WF-e) with matrix coefficients and solution variables defined on original computational mesh, and a newly proposed mapping using all WF mesh (WF-all), on which matrix coefficients and solution variables are defined. Both the P-ADI and the P-SIP have been integrated into a two-dimensional (2D) hydrodynamic model, the CCHE2D (Center of Computational Hydroscience and Engineering) model, developed by the National Center for Computational Hydroscience and Engineering at the University of Mississippi. This study for the first time compared these two parallel solvers and their efficiency using examples and applications in complex geometries, which can provide valuable guidance for future uses of these two parallel implicit solvers in computational fluids dynamics (CFD). Both parallel solvers demonstrated higher efficiency than their serial counterparts on the CPU (Central Processing Unit): 3.73~4.98 speedup ratio for flow simulations, and 2.166~3.648 speedup ratio for sediment transport simulations. In general, the P-ADI solver is faster than but not as stable as the P-SIP solver; and for the P-SIP solver, the newly developed mapping method WF-all significantly improved the conventional mapping method WF-e. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Fluids)
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