Mapundi Banda
University of Pretoria, Mathematics and Applied Mathematics, Faculty Member
Research Interests:
Research Interests:
Industrial Mathematics has established itself as an important branch of professional mathematics. Mathematicians are aware of the need to bridge the gap between highly specialised mathematical research and the high demand for innovation... more
Industrial Mathematics has established itself as an important branch of professional mathematics. Mathematicians are aware of the need to bridge the gap between highly specialised mathematical research and the high demand for innovation from industry. In this presentation we discuss the experiences at the Mathematics in Industry Study Group-South Africa (MISGSA) which has become an annual event. Case studies of
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We present a high-order accurate relaxed non-oscillatory scheme for solving magnetohydrodynamic (MHD) equations. The computations reported here demonstrate the remarkable simplicity and versatility of semi-discrete relaxation schemes as... more
We present a high-order accurate relaxed non-oscillatory scheme for solving magnetohydrodynamic (MHD) equations. The computations reported here demonstrate the remarkable simplicity and versatility of semi-discrete relaxation schemes as solvers for ideal MHD equations. Simulations will be presented for two prototype MHD problems, the one-dimensional Brio–Wu shock tube problems. A qualitative comparison reveals an excellent agreement with previous results based on
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Research Interests:
Research Interests:
ABSTRACT Lattice Boltzmann equations are usually constructed to satisfy some physical requirements such as Galilean invariance and isotropy, to possess a velocity-independent pressure and no compressible effects, and so on. In this paper,... more
ABSTRACT Lattice Boltzmann equations are usually constructed to satisfy some physical requirements such as Galilean invariance and isotropy, to possess a velocity-independent pressure and no compressible effects, and so on. In this paper, a stability requirement is introduced as a new criterion for the constructions. With this requirement, we derive some relations of parameters for several lattice Boltzmann models. Interestingly, these relations are satisfied by many choices of parameters used in the literature.
Research Interests:
Research Interests:
A relaxation system based on a Lattice-Boltzmann type discrete velocity model is considered in the low Mach number limit. A third order relaxation scheme is developed working uniformly for all ranges of the mean free path and Mach number.... more
A relaxation system based on a Lattice-Boltzmann type discrete velocity model is considered in the low Mach number limit. A third order relaxation scheme is developed working uniformly for all ranges of the mean free path and Mach number. In the incompressible Navier-Stokes limit the scheme reduces to an explicit high order finite difference scheme for the incompressible Navier-Stokes equations based on nonoscillatory upwind discretization. Numerical results and comparisons with other approaches are presented for several test cases in one and two space dimensions.
Research Interests: Applied Mathematics, Monte Carlo, Numerical Analysis, Mixing, Non Linear Dynamics, and 13 moreLaminar Microflows, Lattice Boltzmann, Navier Stokes, Lattice Boltzmann Method, Finite Difference Method, Numerical Analysis and Computational Mathematics, Granular Media, Low Mach Number, Lattice Boltzmann Equations, Runge Kutta Methods, Relaxation Scheme, Mach Number, and Finite Difference Scheme
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The convection-radiation effects in thermal fluid flows are studied based on the lattice-Boltzmann method. Nine-velocity flow and temperature distributions are used to obtain the mass, momentum and energy equations in thermal... more
The convection-radiation effects in thermal fluid flows are studied based on the lattice-Boltzmann method. Nine-velocity flow and temperature distributions are used to obtain the mass, momentum and energy equations in thermal incompressible flows by studying equivalent moment systems. The radiative heat flux in the energy equation is obtained using the discrete-ordinates solution of the radiative transfer equation. A non-oscillatory relaxation scheme is used to solve the coupled moment equations. Such schemes have the advantage of being simple and easy to implement. Numerical results are presented for two test examples on coupled convection-radiation flows in two dimensional enclosures. Detailed simulation results at different flow and radiative regimes, as well as benchmark solutions, are presented and discussed.
Research Interests: Engineering, Computational Physics, Convection, Heat Transfer, Mathematical Sciences, and 17 moreNatural Convection, Physical sciences, Heat Flux, Lattice Boltzmann, Fluid flow, Temperature Distribution, Radiative Heat Transfer, Lattice Boltzmann Method, Radiation Effect, Radiative Transfer, Thermal Radiation, Flow Velocity, Energy Transfer, Calculation, Forced Convection, Incompressible Flow, and Relaxation Scheme
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Research Interests:
ABSTRACT Suitable numerical discretizations for boundary control problems of systems of nonlinear hyperbolic partial differential equations are presented. Using a discrete Lyapunov function, exponential decay of the discrete solutions of... more
ABSTRACT Suitable numerical discretizations for boundary control problems of systems of nonlinear hyperbolic partial differential equations are presented. Using a discrete Lyapunov function, exponential decay of the discrete solutions of a system of hyperbolic equations for a family of first-order finite volume schemes is proved. The decay rates are explicitly stated. The theoretical results are accompanied by computational results.
In the computation of approximate solutions to hyperbolic conservation laws, relaxation schemes have proven to be very useful. In this paper we present a new higher order relaxation scheme based on higher order nonoscillatory central... more
In the computation of approximate solutions to hyperbolic conservation laws, relaxation schemes have proven to be very useful. In this paper we present a new higher order relaxation scheme based on higher order nonoscillatory central space discretization and higher order time discretization without use of Riemann solvers. Numerical experiments with 2D Euler systems of gas dynamics are presented to demonstrate
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
ABSTRACT Lattice Boltzmann equations are usually constructed to satisfy some physical requirements such as Galilean invariance and isotropy, to possess a velocity-independent pressure and no compressible effects, and so on. In this paper,... more
ABSTRACT Lattice Boltzmann equations are usually constructed to satisfy some physical requirements such as Galilean invariance and isotropy, to possess a velocity-independent pressure and no compressible effects, and so on. In this paper, a stability requirement is introduced as a new criterion for the constructions. With this requirement, we derive some relations of parameters for several lattice Boltzmann models. Interestingly, these relations are satisfied by many choices of parameters used in the literature.
Research Interests:
Research Interests:
ABSTRACT The goal of this paper is to present an efficient approach for dynamic compressor optimization in gas networks based on a space mapping approach. For the fine space a non-linear isothermal gas flow model is employed, whereas for... more
ABSTRACT The goal of this paper is to present an efficient approach for dynamic compressor optimization in gas networks based on a space mapping approach. For the fine space a non-linear isothermal gas flow model is employed, whereas for the coarse-space model an algebraic model is applied. To solve an optimization problem with the nonlinear model is expensive. Nevertheless we desire to bring as much nonlinear effects into the optimization process as possible. The mathematical formulation and algorithmic aspects of a space mapping technique are developed. A framework in which such can be achieved for compressible isothermal gas flow is presented. Computational results and comparison between different approaches are presented. The results demonstrate that such a multi-level approach provides more accurate results efficiently. Copyright © 2010 John Wiley & Sons, Ltd.
Research Interests:
Research Interests:
Research Interests: Applied Mathematics, Monte Carlo, Numerical Analysis, Mixing, Non Linear Dynamics, and 13 moreLaminar Microflows, Lattice Boltzmann, Navier Stokes, Lattice Boltzmann Method, Finite Difference Method, Numerical Analysis and Computational Mathematics, Granular Media, Low Mach Number, Lattice Boltzmann Equations, Runge Kutta Methods, Relaxation Scheme, Mach Number, and Finite Difference Scheme
ABSTRACT We consider a multiscale network of natural gas pipelines. Different arcs of the network are to be modeled by possibly different models depending on the requisite qualitative detail required: an isothermal Euler system of... more
ABSTRACT We consider a multiscale network of natural gas pipelines. Different arcs of the network are to be modeled by possibly different models depending on the requisite qualitative detail required: an isothermal Euler system of equations; linearized model derived from the isothermal Euler system or a steady-state model of gas flow also referred to as an algebraic model. At the vertices (or joints) of the network coupling conditions are defined. An analysis of the well posedness of the hierarchial coupling conditions is presented. The analytical results are tested numerically on different network configurations including a real-world network based on the Canadian mainline gas network. Copyright © 2007 John Wiley & Sons, Ltd.