Mapundi K. Banda
University of Pretoria
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Publication
Featured researches published by Mapundi K. Banda.
Networks and Heterogeneous Media | 2006
Mapundi K. Banda; Michael Herty; Axel Klar
We introduce a model for gas flow in pipeline networks based on the isothermal Euler equations. We model the intersection of multiple pipes by posing an additional assumption on the pressure at the interface. We give a method to obtain solutions to the gas network problem and present numerical results for sample networks.
Networks and Heterogeneous Media | 2006
Mapundi K. Banda; Michael Herty; Axel Klar
We investigate coupling conditions for gas transport in networks where the governing equations are the isothermal Euler equations. We discuss intersections of pipes by considering solutions to Riemann problems. We introduce additional assumptions to obtain a solution near the intersection and we present numerical results for sample networks.
Journal of Numerical Mathematics | 2005
Mapundi K. Banda; Mohammed Seaïd
We present a higher order generalization for relaxation methods in the framework presented by Jin and Xin in [10]. The schemes employ general higher order integration for spatial discretization and higher order implicit-explicit (IMEX) schemes or Total Variation diminishing (TVD) Runge–Kutta schemes for time integration of relaxing or relaxed schemes, respectively, for time integration. Numerical experiments are performed on various test problems, in particular, the Burgers and Euler equations of inviscid gas dynamics in both one and two space dimensions. In addition, uniform convergence with respect to the relaxation parameter is demonstrated.
SIAM Journal on Scientific Computing | 2005
Mapundi K. Banda; W. A. Yong; Axel Klar
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.
Computational Optimization and Applications | 2012
Mapundi K. Banda; Michael Herty
Starting from relaxation schemes for hyperbolic conservation laws we derive continuous and discrete schemes for optimization problems subject to nonlinear, scalar hyperbolic conservation laws. We discuss properties of first- and second-order discrete schemes and show their relations to existing results. In particular, we introduce first and second-order relaxation and relaxed schemes for both adjoint and forward equations. We give numerical results including tracking type problems with non-smooth desired states.
SIAM Journal on Scientific Computing | 2009
Mapundi K. Banda; Michael Herty; Jean-Medard T. Ngnotchouye
Dynamics of multiphase flows through networks are considered. The dynamics of flow through the connected arcs are governed by an isothermal no-slip drift-flux model. Such problems arise in the context of multicomponent flows or in gas transport in pipe networks in which a phase change takes place due to geometrical or physical forces. Coupling conditions for the vertices (joints) in a network have been proposed. We present conditions at and introduce a mathematical representation of the vertex flow for the no-slip drift-flux case of multiphase flows. Mathematical analysis of coupling conditions at the vertices as well as numerical simulations and comparative studies with theoretical predictions are undertaken.
international conference on computational science | 2002
Mapundi K. Banda; Mohammed Seaïd
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 the remarkable accuracy of the relaxation scheme.
Computational & Applied Mathematics | 2011
Jean Medard T. Ngnotchouye; Michael Herty; Sonja Steffensen; Mapundi K. Banda
The treatment of control problems governed by systems of conservation laws poses serious challenges for analysis and numerical simulations. This is due mainly to shock waves that occur in the solution of nonlinear systems of conservation laws. In this article, the problem of the control of Euler flows in gas dynamics is considered. Numerically, two semi-linear approximations of the Euler equations are compared for the purpose of a gradient-based algorithm for optimization. One is the Lattice-Boltzmann method in one spatial dimension and five velocities (D1Q5 model) and the other is the relaxation method. An adjoint method is used. Good results are obtained even in the case where the solution contains discontinuities such as shock waves or contact discontinuities.
Journal of Scientific Computing | 2016
Mapundi K. Banda; Axel-Stefan Häck; Michael Herty
We consider numerical schemes for
SIAM Journal on Scientific Computing | 2008
Mapundi K. Banda; Mohammed Seaïd; Ioan Teleaga