By Jean-Jacques Chattot
ISBN-10: 3642077986
ISBN-13: 9783642077982
ISBN-10: 3662050641
ISBN-13: 9783662050644
This textbook is written for senior undergraduate and graduate scholars in addition to engineers who will strengthen or use code within the simulation of fluid flows or different actual phenomena. the target of the booklet is to offer the reader the foundation for figuring out the way in which numerical schemes in achieving actual and reliable simulations of actual phenomena. it's according to the finite-difference technique and straightforward adequate difficulties that let additionally the analytic ideas to be labored out. ODEs in addition to hyperbolic, parabolic and elliptic varieties are handled. The reader will also discover a bankruptcy at the options of linearization of nonlinear difficulties. the ultimate bankruptcy applies the fabric to the equations of gasoline dynamics. The ebook builds on basic version equations and, pedagogically, on a bunch of difficulties given including their solutions.
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Extra resources for Computational Aerodynamics and Fluid Dynamics: An Introduction
Example text
10) can be interpreted as a vector dot product, 38 4. Partial Differential Equations t 2 /////// /////// /////// /////// /////// /////// /////// /////// /////// /////// /////// /////// /////// /////// x -1 Fig. 1. Moving shock with Burgers' equation v. \7 ¢ = 0, stating that the characteristic lines are tangent to the vector field V. e. ° { u(x,O) = 0, x < u(x, 0) = 1, x> 0. an expansion shock is ruled out, as violating the condition that characteristics must originate from the initial condition, and cannot appear in the middle of the domain.
Remark: When (J = 1, the TE is identically zero. The scheme reads 'PH1,j = -'Pi-l,j + 'Pi,j+l + 'Pi,j-l· Note first that the characteristics coincide with the diagonals of the mesh system. If we assume that the values 'Pi,j'S in the right-hand side are exact, then, using d'Alembert solution However, from the exact solution hence 'PH1,j = FH1,j + Gi +1,j, ° which is the exact solution. Since the values of 'PO,j and 'Pl,j are exact, it follows that all the values in the triangle bounded by ~ = and 'f/ = 'f/max will be exact (zero in the present problem).
In terms of :S (3Lly, a CFL condition for the "time step" Llx, for a given Lly. Remark: When (J = 1, the TE is identically zero. The scheme reads 'PH1,j = -'Pi-l,j + 'Pi,j+l + 'Pi,j-l· Note first that the characteristics coincide with the diagonals of the mesh system. If we assume that the values 'Pi,j'S in the right-hand side are exact, then, using d'Alembert solution However, from the exact solution hence 'PH1,j = FH1,j + Gi +1,j, ° which is the exact solution. Since the values of 'PO,j and 'Pl,j are exact, it follows that all the values in the triangle bounded by ~ = and 'f/ = 'f/max will be exact (zero in the present problem).
Computational Aerodynamics and Fluid Dynamics: An Introduction by Jean-Jacques Chattot
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