High-Order Numerical Methods for Solving Full Compressible Navier–Stokes Equations with Moving Boundaries and Temperature-Dependent Heat Conductivity
Sharapov R. Mikhailov V. Niyazymbetov A. Bazil G. Kuzina N.
December 2025International Information and Engineering Technology Association
International Journal of Heat and Technology
2025#43Issue 61997 - 2003 pp.
The goal of this research is to develop and validate new computational approaches to enhance our understanding of fluid dynamics. To provide more accurate tools for industrial operations, meteorology, and aeronautical engineering, we address the limitations of existing methods. We employed third-order Runge-Kutta methods with Total Variation Diminishing (TVD) for temporal integration, fifth-order Weighted Essentially Non-Oscillatory (WENO) schemes for spatial discretization, as well as Finite Volume Methods (FVM) and Finite Element Methods (FEM) as advanced numerical techniques. The novelty of this work lies in integrating high-order WENO schemes with FEM and AMR for full compressible Navier–Stokes equations with moving boundaries and temperature-dependent heat conductivity, which has not been previously addressed in the literature. Additionally, high-performance computing methods, moving mesh approaches, and Adaptive Mesh Refinement (AMR) were utilized. The results demonstrate significant improvements in both the efficiency and accuracy of the simulations. Specifically, compared to traditional second-order methods, the fifth-order WENO schemes reduced errors by a factor of four. Furthermore, it was shown that the new schemes enhanced the accuracy of capturing discontinuities and fine-scale structures, maintaining a variation of less than 1% from analytical solutions, while reducing computational complexity by up to 30% and processing time by approximately 25%. These findings suggest that the proposed WENO schemes offer multiple valuable advantages for high-precision applications in hydrodynamics and aeronautical engineering, which solve hyperbolic conservation laws.
Adaptive Mesh Refinement (AMR) , aerospace engineering simulation , computational methods , high-order WENO scheme , hydrodynamics , numerical stability
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Department of Water Supply and Water Disposal, Moscow State University of Civil Engineering (National Research University), Moscow, 129337, Russian Federation
Department of System Analysis and Information Technologies, Kazan Privolzhsky Federal University, Kazan, 420043, Russian Federation
Department of Math, NJSC South Kazakhstan Pedagogical University Named after Ozbekali Zhanibekov, Shymkent, 160012, Kazakhstan
Department of Automation and Control, Almaty University of Power Engineering and Telecommunications, Almaty, 050013, Kazakhstan
Department of Physics, Kazan National Research Technological University, Kazan, 420015, Russian Federation
Department of Water Supply and Water Disposal
Department of System Analysis and Information Technologies
Department of Math
Department of Automation and Control
Department of Physics
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