High resolution upwind and centered methods are a mature generation of computational techniques. They are applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. For its third edition the book has been thoroughly revised to contain new material.
High resolution upwind and centered methods are a mature generation of computational techniques. They are applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. For its third edition the book has been thoroughly revised to contain new material.
The Equations of Fluid Dynamics. Notions on Hyperbolic Partial Differential Equations. Some Properties of the Euler Equations. The Riemann Problem for the Euler Equations. Notions on Numerical Methods. The Method of Godunov for Non#x2014;linear Systems. Random Choice and Related Methods. Flux Vector Splitting Methods. Approximate#x2014;State Riemann Solvers. The HLL and HLLC Riemann Solvers. The Riemann Solver of Roe. The Riemann Solver of Osher. High#x2013;Order and TVD Methods for Scalar Equations. High#x2013;Order and TVD Schemes for Non#x2013;Linear Systems. Splitting Schemes for PDEs with Source Terms. Methods for Multi#x2013;Dimensional PDEs. Multidimensional Test Problems. FORCE Fluxes in Multiple Space Dimensions. The Generalized Riemann Problem. The ADER Approach. Concluding Remarks.
The Equations of Fluid Dynamics. Notions on Hyperbolic Partial Differential Equations. Some Properties of the Euler Equations. The Riemann Problem for the Euler Equations. Notions on Numerical Methods. The Method of Godunov for Non#x2014;linear Systems. Random Choice and Related Methods. Flux Vector Splitting Methods. Approximate#x2014;State Riemann Solvers. The HLL and HLLC Riemann Solvers. The Riemann Solver of Roe. The Riemann Solver of Osher. High#x2013;Order and TVD Methods for Scalar Equations. High#x2013;Order and TVD Schemes for Non#x2013;Linear Systems. Splitting Schemes for PDEs with Source Terms. Methods for Multi#x2013;Dimensional PDEs. Multidimensional Test Problems. FORCE Fluxes in Multiple Space Dimensions. The Generalized Riemann Problem. The ADER Approach. Concluding Remarks.
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