Browsing by Author "Titarev, Vladimir A."

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    Conservative numerical methods for model kinetic equations
    (Elsevier, 2007-11) Titarev, Vladimir A.
    A new conservative discrete ordinate method for nonlinear model kinetic equations is proposed. The conservation property with respect to the collision integral is achieved by satisfying at the discrete level approximation conditions used in deriving the model collision integrals. Additionally to the conservation property, the method ensures the correct approximation of the heat fluxes. Numerical examples of flows with large gradients are provided for the Shakhov and Rykov model kinetic equations.
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    Exact and approximate solutions of Riemann problems in non-linear elasticity
    (Elsevier, 2009-10-01) Barton, Philip Trevor; Drikakis, Dimitris; Romenski, E.; Titarev, Vladimir A.
    Eulerian shock-capturing schemes have advantages for modelling problems involving complex non-linear wave structures and large deformations in solid media. Various numerical methods now exist for solving hyperbolic conservation laws that have yet to be applied to non-linear elastic theory. In this paper one such class of solver is examined based upon characteristic tracing in conjunction with high-order monotonicity preserving weighted essentially non-oscillatory (MPWENO) reconstruction. Furthermore, a new iterative method for finding exact solutions of the Riemann problem in non-linear elasticity is presented. Access to exact solutions enables an assessment of the performance of the numerical techniques with focus on the resolution of the seven wave structure. The governing model represents a special case of a more general theory describing additional physics such as material plasticity. The numerical scheme therefore provides a firm basis for extension to simulate more complex physical phenomena. Comparison of exact and numerical solutions of one-dimensional initial values problems involving three-dimensional deformations is presented.
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    Uniformly high-order schemes on arbitrary unstructured meshes for advection diffusion
    (Elsevier, 2011-07) Titarev, Vladimir A.; Drikakis, Dimitris
    The paper presents a linear high-order method for advection-di®usion conser- vation laws on three dimensional mixed-element unstructured meshes. The key ingredient of the method is a reconstruction procedure in local compu- tational coordinates. Numerical results illustrate the convergence rates for the linear equation and a non-linear hyperbolic system with di®usion terms for various types of meshes.
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    WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions
    (Elsevier, 2010-11-23) Tsoutsanis, Panagiotis; Titarev, Vladimir A.; Drikakis, Dimitris
    The paper extends weighted essentially non-oscillatory (WENO) methods to three dimensional mixed-element unstructured meshes, comprising tetrahedral, hexahedral, prismatic and pyramidal elements. Numerical results illustrate the convergence rates and non-oscillatory properties of the schemes for various smooth and discontinuous solutions test cases and the compressible Euler equations on various types of grids. Schemes of up to fifth order of spatial accuracy are considered.