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Double-diffusive convection in a Darcy–Brinkman porous layer with higher-order thermal and solutal diffusion.

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Title:	Double-diffusive convection in a Darcy–Brinkman porous layer with higher-order thermal and solutal diffusion.
Authors:	Khalaf, Sanaa L.¹ (AUTHOR) sanaasanaa1978@yahoo.com, Harfash, Akil Jassim¹ (AUTHOR) akilharfash@gmail.com
Source:	International Journal of Numerical Methods for Heat & Fluid Flow. 2026, Vol. 36 Issue 5, p1993-2026. 34p.
Subjects:	Stability of linear systems, Stability of nonlinear systems, Thermal instability, Porous materials, Numerical analysis, Concentration gradient, Thermal conductivity
Abstract:	Purpose: The purpose of this study is to analyse double-diffusive convection in a fluid-saturated porous layer using an extended Darcy–Brinkman model with higher-order (bi-Laplacian) thermal and solutal diffusion and to determine linear and nonlinear stability thresholds. Design/methodology/approach: The governing equations are nondimensionalised and linearised about the conduction state to obtain the perturbation equations. Linear instability analysis was performed, and a nonlinear energy stability analysis was developed to determine unconditional decay thresholds for perturbations. The instability and nonlinear thresholds are computed using two high-accuracy Chebyshev collocation methods (standard and boundary-fitted). Findings: Brinkman viscous diffusion and higher-order thermal/solutal diffusion act predominantly as stabilising mechanisms: they increase the critical Rayleigh numbers, reshape the neutral curves and shift the stationary–oscillatory transition in parameter space. The nonlinear (energy) threshold is consistently lower than the linear threshold, identifying a conditional-stability interval RaE < Ra < RaL in which linear stability holds but unconditional nonlinear decay is not guaranteed by the present energy estimate. In the top-heavy solutal configuration, higher-order solutal diffusion provides the strongest suppression of solutal-driven fingering. Both numerical schemes exhibit spectral convergence; however, the boundary-fitted method achieves smaller residuals at the same truncation order, indicating improved accuracy and efficiency. Originality/value: To the best of the authors' knowledge, this is the first combined linear/energy stability study of thermosolutal convection in a Darcy–Brinkman porous layer with higher-order thermal and solutal diffusion, supported by spectrally accurate Chebyshev collocation schemes for the associated high-order eigenvalue problems. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	Purpose: The purpose of this study is to analyse double-diffusive convection in a fluid-saturated porous layer using an extended Darcy–Brinkman model with higher-order (bi-Laplacian) thermal and solutal diffusion and to determine linear and nonlinear stability thresholds. Design/methodology/approach: The governing equations are nondimensionalised and linearised about the conduction state to obtain the perturbation equations. Linear instability analysis was performed, and a nonlinear energy stability analysis was developed to determine unconditional decay thresholds for perturbations. The instability and nonlinear thresholds are computed using two high-accuracy Chebyshev collocation methods (standard and boundary-fitted). Findings: Brinkman viscous diffusion and higher-order thermal/solutal diffusion act predominantly as stabilising mechanisms: they increase the critical Rayleigh numbers, reshape the neutral curves and shift the stationary–oscillatory transition in parameter space. The nonlinear (energy) threshold is consistently lower than the linear threshold, identifying a conditional-stability interval RaE < Ra < RaL in which linear stability holds but unconditional nonlinear decay is not guaranteed by the present energy estimate. In the top-heavy solutal configuration, higher-order solutal diffusion provides the strongest suppression of solutal-driven fingering. Both numerical schemes exhibit spectral convergence; however, the boundary-fitted method achieves smaller residuals at the same truncation order, indicating improved accuracy and efficiency. Originality/value: To the best of the authors' knowledge, this is the first combined linear/energy stability study of thermosolutal convection in a Darcy–Brinkman porous layer with higher-order thermal and solutal diffusion, supported by spectrally accurate Chebyshev collocation schemes for the associated high-order eigenvalue problems. [ABSTRACT FROM AUTHOR]
ISSN:	09615539