Zhenhua Jiang^1,*, Xi Deng^2,3, Xin Zhang¹, Chao Yan¹, Feng Xiao⁴, Jian Yu¹

FDMP-Fluid Dynamics & Materials Processing, Vol.20, No.10, pp. 2183-2204, 2024, DOI:10.32604/fdmp.2024.053231

Abstract Shock waves, characterized by abrupt changes in pressure, temperature, and density, play a significant role in various materials science processes involving fluids. These high-energy phenomena are utilized across multiple fields and applications to achieve unique material properties and facilitate advanced manufacturing techniques. Accurate simulations of these phenomena require numerical schemes that can represent shock waves without spurious oscillations and simultaneously capture acoustic waves for a wide range of wavelength scales. This work suggests a high-order discontinuous Galerkin (DG) method with a finite volume (FV) subcell limiting strategies to achieve better subcell resolution and lower numerical More >

Saad Adjal^1,*, Sabiha Aklouche-Benouaguef¹, Belkacem Zeghmati²

FDMP-Fluid Dynamics & Materials Processing, Vol.18, No.5, pp. 1389-1397, 2022, DOI:10.32604/fdmp.2022.021619

Abstract Two-dimensional transient laminar natural convection in a square cavity containing a porous medium and inclined at an angle of 30∘ is investigated numerically. The vertical walls are differentially heated, and the horizontal walls are adiabatic. The effect of Rayleigh number on heat transfer and on the road to chaos is analyzed. The natural heat transfer and the Darcy Brinkman equations are solved by using a finite volume method and a Tri Diagonal Matrix Algorithm (TDMA). The results are obtained for a porosity equal to 0.45, a Darcy number and a Prandtl respectively equal to 10⁻³ and More >

Sheikh Hassan¹, Didarul Ahasan Redwan¹, Md. Mamun Molla^1,2,*, Sharaban Thohura³, M. Abu Taher⁴, Sadia Siddiqa⁵

Energy Engineering, Vol.118, No.6, pp. 1659-1679, 2021, DOI:10.32604/EE.2021.017657

Abstract A two-dimensional (2D) laminar flow of nanofluids confined within a square cavity having localized heat source at the bottom wall has been investigated. The governing Navier–Stokes and energy equations have been non dimensionalized using the appropriate non dimensional variables and then numerically solved using finite volume method. The flow was controlled by a range of parameters such as Rayleigh number, length of heat source and nanoparticle volume fraction. The numerical results are represented in terms of isotherms, streamlines, velocity and temperature distribution as well as the local and average rate of heat transfer. A comparative More >

Yanlong Zhang¹, Yanhui Zhou², Jiming Wu^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.2, pp. 487-514, 2021, DOI:10.32604/cmes.2021.014950

Abstract In this article, we study a 2D nonlinear time-fractional Rayleigh-Stokes problem, which has an anomalous sub-diffusion term, on triangular meshes by quadratic finite volume element schemes. Time-fractional derivative, defined by Caputo fractional derivative, is discretized through formula, and a two step scheme is used to approximate the time first-order derivative at time , where the nonlinear term is approximated by using a matching linearized difference scheme. A family of quadratic finite volume element schemes with two parameters are proposed for the spatial discretization, where the range of values for two parameters are , . For More >

Daiane Cristina Zanatta^1,*, Luciano Kiyoshi Araki², Marcio Augusto Villela Pinto², Diego Fernando Moro³

CMES-Computer Modeling in Engineering & Sciences, Vol.125, No.3, pp. 1061-1081, 2020, DOI:10.32604/cmes.2020.012634

Abstract This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry. For this, the differential equations were discretized by Finite Volume Method (FVM) with second-order approximation scheme and deferred correction. Moreover, the algebraic method and the differential method were used to generate the non-orthogonal structured curvilinear grids. Furthermore, the influence of some parameters of geometric multigrid method, as well as lexicographical Gauss–Seidel (Lex-GS), η-line Gauss–Seidel (η-line-GS), Modified Strongly Implicit (MSI) and modified incomplete LU decomposition (MILU) solvers on the Central Processing… More >

Mengya Su¹, Zhihao Ren¹, Zhiyue Zhang^{1, *}

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.2, pp. 739-776, 2020, DOI:10.32604/cmes.2020.08563

Abstract Based on rectangular partition and bilinear interpolation, we construct an alternating-direction implicit (ADI) finite volume element method, which combined the merits of finite volume element method and alternating direction implicit method to solve a viscous wave equation with variable coefficients. This paper presents a general procedure to construct the alternating-direction implicit finite volume element method and gives computational schemes. Optimal error estimate in L² norm is obtained for the schemes. Compared with the finite volume element method of the same convergence order, our method is more effective in terms of running time with the increasing of More >

Huawen Shu, Minghai Xu, Xinyue Duan^*, Yongtong Li, Yu Sun, Ruitian Li, Peng Ding

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.2, pp. 509-523, 2020, DOI:10.32604/cmes.2020.08806

Abstract A finite volume method based unstructured grid is presented to solve the two dimensional viscous and incompressible flow. The method is based on the pressure-correction concept and solved by using a semi-staggered grid technique. The computational procedure can handle cells of arbitrary shapes, although solutions presented in this paper were only involved with triangular and quadrilateral cells. The pressure or pressure-correction value was stored on the vertex of cells. The mass conservation equation was discretized on the dual cells surrounding the vertex of primary cells, while the velocity components and other scale variables were saved More >

Nouri Sabrina^1,*, Abderrahmane Ghezal¹, Said Abboudi², Pierre Spiteri³

FDMP-Fluid Dynamics & Materials Processing, Vol.14, No.2, pp. 121-135, 2018, DOI:10.3970/fdmp.2018.02045

Abstract This paper deals with the numerical study of heat and mass transfer occurring in a cavity filled with a low Prandtl number liquid. The model includes the momentum, energy and mass balance equations. These equations are discretized by a finite volume technique and solved in the framework of a custom SIMPLER method developed in FORTRAN. The effect of the problem characteristic parameters, namely the Lewis and Prandtl numbers, on the instability of the flow and related solute distribution is studied for positive and negative thermal and solutal buoyancy forces ratio. Nusselt and Sherwood numbers are More >

C. G. Mohan, A. Satheesh^*

Frontiers in Heat and Mass Transfer, Vol.8, pp. 1-13, 2017, DOI:10.5098/hmt.8.36

Abstract In this study, a two-dimensional steady state double-diffusive mixed convective flow in a square cavity with Soret effect is presented. The numerical investigation is considered with two different conditions, (a) top and bottom walls move with same velocity (Uo) towards right and (b) top wall moves towards right and bottom wall moves towards left with the same velocity (Uo). The left and right walls remain stationary. The top and bottom walls are adiabatic; the left wall is maintained at high temperature and concentration. The right wall is maintained at low temperature and concentration. Governing equations More >

M. Zitoune^{1, 2} , O. Ourrad Meziani², B. Meziani², M. Adnani^{1, 2}

FDMP-Fluid Dynamics & Materials Processing, Vol.12, No.1, pp. 33-55, 2016, DOI:10.3970/fdmp.2016.012.033

Abstract A finite volume code used for detailed analysis of forced-convection flow in a horizontal channel containing eight heat sources simulating electronic components. The study deals the effect of variations of Reynolds number, the volume fraction and the good choice of type of nanoparticles added to the base fluid. The study shows that the rate of heat transfer increases with increasing Reynolds number and the volume fraction of nanofluids but not infinitely. The analysis of the dynamic and thermal field shows that the heat transfer is improved, with the increase in the Reynolds number and the More >