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<p>This work deals with a novel Gaussian filter-based pressure correction technique with a higher-order super-compact (HOSC) finite difference scheme for solving unsteady three-dimensional (3D) incompressible, viscous flows. The proposed pressure correction method offers significant advantages in terms of optimizing computational time by taking minimum iterations to reach the required accuracy, making it highly efficient and cost-effective. Since pressure fields often exhibit strong nonlinear behavior, the application of a Gaussian filter helps reduce numerical noise and fluctuations, thereby improving the reliability of the results. The HOSC scheme achieves second-order accuracy in time and fourth-order accuracy in space while using a minimal number of grid points. Specifically, it employs 19 grid points from the known time level (i.e., <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n\textrm{th}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mtext>th</mtext> </mrow> </math></EquationSource> </InlineEquation> time level) and only seven from the unknown time level (i.e., <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n+1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> time level). This compact structure contributes to reduced computational costs without compromising the accuracy of the solution. We have implemented our methodology across three distinct scenarios: the 3D Burger’s equation having analytical solution, and two variations of the lid-driven cavity problem. The simulation results show excellent agreement with both the analytical solutions and previously published numerical results. This strong consistency highlights the accuracy and robustness of the proposed approach. Additionally, we conducted a detailed analysis of the pressure correction method using streamline contours and pressure field visualizations. The findings of this study have significant implications for various engineering and scientific disciplines, such as aerodynamics, hydrodynamics, and fluid–structure interaction analysis.</p>

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A novel Gaussian filter-based pressure correction technique with higher-order super-compact scheme for unsteady 3D incompressible, viscous flows

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Ashwani Punia,
  • Rajendra K. Ray

摘要

This work deals with a novel Gaussian filter-based pressure correction technique with a higher-order super-compact (HOSC) finite difference scheme for solving unsteady three-dimensional (3D) incompressible, viscous flows. The proposed pressure correction method offers significant advantages in terms of optimizing computational time by taking minimum iterations to reach the required accuracy, making it highly efficient and cost-effective. Since pressure fields often exhibit strong nonlinear behavior, the application of a Gaussian filter helps reduce numerical noise and fluctuations, thereby improving the reliability of the results. The HOSC scheme achieves second-order accuracy in time and fourth-order accuracy in space while using a minimal number of grid points. Specifically, it employs 19 grid points from the known time level (i.e., \(n\textrm{th}\) n th time level) and only seven from the unknown time level (i.e., \(n+1\) n + 1 time level). This compact structure contributes to reduced computational costs without compromising the accuracy of the solution. We have implemented our methodology across three distinct scenarios: the 3D Burger’s equation having analytical solution, and two variations of the lid-driven cavity problem. The simulation results show excellent agreement with both the analytical solutions and previously published numerical results. This strong consistency highlights the accuracy and robustness of the proposed approach. Additionally, we conducted a detailed analysis of the pressure correction method using streamline contours and pressure field visualizations. The findings of this study have significant implications for various engineering and scientific disciplines, such as aerodynamics, hydrodynamics, and fluid–structure interaction analysis.