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Shamsul Qamar - One of the best experts on this subject based on the ideXlab platform.

  • Kinetic Flux Vector Splitting scheme for solving non-reactive multi-component flows.
    Computational Biology and Chemistry, 2019
    Co-Authors: Muhammad Saqib, Attia Rabbani, Ubaid Ahmed Nisar, Waqas Ashraf, Shamsul Qamar
    Abstract:

    Abstract This paper is about multi-component flow. There is no doubt that multi-component flow has a wide range of applications, specially in aerospace it plays a vital role during reentry of space ship into earth's atmosphere thats why it cannot be neglected for a proper vehicle design. In this paper one- and two-dimensional homogenous multi-component flow models are numerically investigated by using a high resolution Splitting scheme and this scheme is known as Kinetic Flux Vector Splitting scheme. This scheme preserves positivity conditions and resolves shocks, rarefaction and contact discontinuity. The scheme is based on Splitting of Flux functions. Moreover Runge-Kutta time stepping technique with MUSCL-type initial reconstruction is used to guarantee higher order accurate solution. This work is first done by Qamar and Warnecke (2004) for the homogeneous multi-component flow equations using central scheme, here we investigate the same work using kinetic Flux Vector Splitting scheme (KFVS) and compared the results with central scheme to verify the efficiency of studied scheme.

  • A kinetic Flux Vector Splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients.
    PloS one, 2018
    Co-Authors: M. Rehan Saleem, Waqas Ashraf, Saqib Zia, Ishtiaq Ali, Shamsul Qamar
    Abstract:

    This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic Flux Vector Splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme.

  • Application of Kinetic Flux Vector Splitting Scheme for Solving Viscous Quantum Hydrodynamical Model of Semiconductor Devices
    2018
    Co-Authors: Ubaid Ahmed Nisar, Waqas Ashraf, Shamsul Qamar
    Abstract:

    In this article, one-dimensional viscous quantum hydrodynamical model of semiconductor devices is numerically investigated. The model treats the propagation of electrons in a semiconductor device as the flow of a charged compressible fluid. It plays an important role in predicting the behavior of electron flow in semiconductor devices. The nonlinear viscous quantum hydrodynamic models contain Euler-type equations for density and current, viscous and quantum correction terms, and a Poisson equation for electrostatic potential. Due to high nonlinearity of model equations, numerical solution techniques are applied to obtain their solutions.. The proposed numerical scheme is a Splitting scheme based on the kinetic Flux-Vector Splitting (KFVS) method for the hyperbolic step, and a semi-implicit Runge-Kutta method for the relaxation step. The KFVS method is based on the direct Splitting of macroscopic Flux functions of the system on the cell interfaces. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge-Kutta time stepping method. Several case studies are considered. For validation, the results of current scheme are compared with those obtained from the Splitting scheme based on the NT central scheme. The effects of various parameters such as device length, viscosities, different doping and voltage are analyzed. The accuracy, efficiency and simplicity of the proposed KFVS scheme validates its generic applicability to the given model equations.

  • Application of kinetic Flux Vector Splitting scheme for solving multi-dimensional hydrodynamical models of semiconductor devices
    Results in Physics, 2017
    Co-Authors: Ubaid Ahmed Nisar, Waqas Ashraf, Shamsul Qamar
    Abstract:

    Abstract In this article, one and two-dimensional hydrodynamical models of semiconductor devices are numerically investigated. The models treat the propagation of electrons in a semiconductor device as the flow of a charged compressible fluid. It plays an important role in predicting the behavior of electron flow in semiconductor devices. Mathematically, the governing equations form a convection–diffusion type system with a right hand side describing the relaxation effects and interaction with a self consistent electric field. The proposed numerical scheme is a Splitting scheme based on the kinetic Flux-Vector Splitting (KFVS) method for the hyperbolic step, and a semi-implicit Runge–Kutta method for the relaxation step. The KFVS method is based on the direct Splitting of macroscopic Flux functions of the system on the cell interfaces. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge–Kutta time stepping method. Several case studies are considered. For validation, the results of current scheme are compared with those obtained from the Splitting scheme based on the NT central scheme. The effects of various parameters such as low field mobility, device length, lattice temperature and voltage are analyzed. The accuracy, efficiency and simplicity of the proposed KFVS scheme validates its generic applicability to the given model equations. A two dimensional simulation is also performed by KFVS method for a MESFET device, producing results in good agreement with those obtained by NT-central scheme.

  • A kinetic Flux-Vector Splitting method for single-phase and two-phase shallow flows
    Computers & Mathematics with Applications, 2014
    Co-Authors: Saqib Zia, Shamsul Qamar
    Abstract:

    A high order kinetic Flux-Vector Splitting method (KFVS) is applied to solve single-phase and two-phase shallow flow equations. The single-phase shallow water equations contain the flow height and momentum. On the other hand, the two-phase flow is considered as a shallow layer of solid granular material and fluid over a horizontal surface. The flow components are assumed to be incompressible and the flow height, solid volume fraction and phase momenta are considered. Our interest lies in the numerical approximation of the above mentioned models, whose complexities pose numerical difficulties. The proposed numerical method is based on the direct Splitting of macroscopic Flux functions of the system of equations. The two-phase shallow flow model governs a non-homogeneous conservation law and, thus, the scheme is extended to account for the non homogeneous cases. The higher order accuracy of the scheme is achieved by using a MUSCL-type initial reconstruction and the Runge-Kutta time stepping method. A number of numerical test problems are considered. For validation, the results of the proposed method are compared with those obtained from the staggered central scheme. The numerical results show the accuracy and robustness of the suggested solver.

Huazhong Tang - One of the best experts on this subject based on the ideXlab platform.

  • steger warming Flux Vector Splitting method for special relativistic hydrodynamics
    Mathematical Methods in The Applied Sciences, 2014
    Co-Authors: Jian Zhao, Huazhong Tang
    Abstract:

    This paper discusses the properties of the rotational invariance and hyperbolicity in time of the governing equations of the ideal special relativistic hydrodynamics and proves for the first time that the ideal relativistic hydrodynamical equations satisfy the homogeneity property, which is the footstone of the Steger–Warming Flux Vector Splitting method [J. L. Steger and R. F. Warming, J. Comput. Phys., 40(1981), 263–293]. On the basis of this remarkable property, the Steger–Warming Flux Vector Splitting (SW-FVS) is given. Two high-resolution SW-FVS schemes are also given on the basis of the initial reconstructions of the solutions and the Fluxes, respectively. Several numerical experiments are conducted to validate the performance of the SW-FVS method. Copyright © 2013 John Wiley & Sons, Ltd.

  • Steger–Warming Flux Vector Splitting method for special relativistic hydrodynamics
    Mathematical Methods in The Applied Sciences, 2013
    Co-Authors: Jian Zhao, Peng He, Huazhong Tang
    Abstract:

    This paper discusses the properties of the rotational invariance and hyperbolicity in time of the governing equations of the ideal special relativistic hydrodynamics and proves for the first time that the ideal relativistic hydrodynamical equations satisfy the homogeneity property, which is the footstone of the Steger–Warming Flux Vector Splitting method [J. L. Steger and R. F. Warming, J. Comput. Phys., 40(1981), 263–293]. On the basis of this remarkable property, the Steger–Warming Flux Vector Splitting (SW-FVS) is given. Two high-resolution SW-FVS schemes are also given on the basis of the initial reconstructions of the solutions and the Fluxes, respectively. Several numerical experiments are conducted to validate the performance of the SW-FVS method. Copyright © 2013 John Wiley & Sons, Ltd.

  • kinetic Flux Vector Splitting for the euler equations with general pressure laws 1
    2004
    Co-Authors: Huazhong Tang
    Abstract:

    This paper attempts to develop kinetic Flux Vector Splitting (KFVS) for the Euler equations with general pressure laws. It is well known that the gas distribution function for the local equilibrium state plays an important role in the construction of the gas–kinetic schemes. To recover the Euler equations with a general equation of state (EOS), a new local equilibrium distribution is introduced with two parameters of temperature approximation decided uniquely by macroscopic variables. Utilizing the well-known connection that the Euler equations of motion are the moments of the Boltzmann equation whenever the velocity distribution function is a local equilibrium state, a class of high resolution MUSCL–type KFVS schemes are presented to approximate the Euler equations of gas dynamics with a general EOS. The schemes are finally applied to several test problems for a general EOS. In comparison with the exact solutions, our schemes give correct location and more accurate resolution of discontinuities. The extension of our idea to multidimensional case is natural.

  • Kinetic Flux Vector Splitting for radiation hydrodynamical equations
    Computers & Fluids, 2000
    Co-Authors: Huazhong Tang, Hua-mo Wu
    Abstract:

    Abstract This paper is interested in the kinetic Flux Vector Splitting (KFVS) for the multidimensional radiation hydrodynamical equations (RHEs) in zero diffusion limit. First, a generalized Maxwell–Boltzmann distribution function with two new parameters of temperature approximation is introduced to recover the macroscopic equations. These parameters are uniquely determined by macroscopic variables. Then, a high resolution KFVS method is proposed for the solution of the multidimensional RHEs. It does not require any Riemann solvers. Finally, several numerical examples are given to show the performance of our scheme.

Np Weatherill - One of the best experts on this subject based on the ideXlab platform.

Qiu-ju Zhang - One of the best experts on this subject based on the ideXlab platform.

  • The implicit formulation of Flux-Vector-Splitting scheme with application to transonic flows
    International Journal of Mechanical Sciences, 2006
    Co-Authors: Qiu-ju Zhang
    Abstract:

    Abstract This paper presents an efficient implicit solver for transonic shock-tube flow, generated for a needle-free epidermal delivery of powdered vaccines. This transient transonic flow exhibits complicated flow phenomena. We proposed a unique method of implicit formation on the basis of analysing a model equation, which can separately deal with convection, diffusion and source terms. By combining this idea with Flux-Vector-Splitting, an implicit Flux-Vector-Splitting solver of the Navier–Stokes equations, which can avoid approximate-factorization (AF) or block-bidiagonalization, is developed. Numerical experiments show that it has obvious superiority over the conventional Flux-Vector-Splitting scheme in terms of convergence and computing cost, meanwhile maintaining a high accuracy and robustness.

Sokrates Tsangaris - One of the best experts on this subject based on the ideXlab platform.

  • Development of an artificial compressibility methodology using Flux Vector Splitting
    International Journal for Numerical Methods in Fluids, 1997
    Co-Authors: Th. Pappou, Sokrates Tsangaris
    Abstract:

    An implicit, upwind arithmetic scheme that is efficient for the solution of laminar, steady, incompressible, two-dimensional flow fields in a generalised co-ordinate system is presented in this paper. The developed algorithm is based on the extended Flux-Vector-Splitting (FVS) method for solving incompressible flow fields. As in the case of compressible flows, the FVS method consists of the decomposition of the convective Fluxes into positive and negative parts that transmit information from the upstream and downstream flow field respectively. The extension of this method to the solution of incompressible flows is achieved by the method of artificial compressibility, whereby an artificial time derivative of the pressure is added to the continuity equation. In this way the incompressible equations take on a hyperbolic character with pseudopressure waves propagating with finite speed. In such problems the ‘information’ inside the field is transmitted along its characteristic curves. In this sense, we can use upwind schemes to represent the finite volume scheme of the problem's governing equations. For the representation of the problem variables at the cell faces, upwind schemes up to third order of accuracy are used, while for the development of a time-iterative procedure a first-order-accurate Euler backward-time difference scheme is used and a second-order central differencing for the shear stresses is presented. The discretized Navier–Stokes equations are solved by an implicit unfactored method using Newton iterations and Gauss–Siedel relaxation. To validate the derived arithmetical results against experimental data and other numerical solutions, various laminar flows with known behaviour from the literature are examined. © 1997 John Wiley & Sons, Ltd.

  • On the solution of the compressible Navier- Stokes equations using improved Flux Vector Splitting methods
    Applied Mathematical Modelling, 1993
    Co-Authors: Dimitris Drikakis, Sokrates Tsangaris
    Abstract:

    Abstract In this paper the accuracy of two Flux Vector Splitting methods using upwind schemes up to the fourth order of accuracy for the solution of the unsteady compressible Navier-Stokes equations is improved. Two of the most well-known methods for the solution of the inviscid gas dynamic equations, the Flux Vector Splitting method by Steger and Warming and the Flux Vector Splitting method by van Leer are presented for the first time in combination with a five-point upwind scheme. Inaccuracies of Flux Vector Splitting methods, which have been presented in the recent literature, can be eliminated using the present schemes in conjunction with proposed corrections for the Flux Splittings. The boundary layers can be approached with high-order accuracy. Investigation of the Flux Vector Splitting method is also carried out in the context of a monotone upstream centered scheme for conservation law forms (MUSCL). The present techniques can be used in compressible viscous flows, predicting with accuracy viscous phenomena such as separation and shock boundary layer interaction. Fast convergence of the implicit method is obtained by solving the system of equations with the Gauss-Seidel relaxation technique. Investigation of the diffusion terms’ discretization scheme is presented.