Numerical methods are indispensable tools in the analysis of complex fluid flows. This book focuses on computational techniques for high-speed gas flows, especially gas flows containing shocks and other steep gradients. The book decomposes complicated numerical methods into simple modular parts, showing how each part fits and how each method relates to or differs from others. The text begins with a review of gasdynamics and computational techniques. Next come basic principles of computational gasdynamics. The last two parts cover basic techniques and advanced techniques. Senior- and graduate-level students, especially in aerospace engineering, as well as researchers and practicing engineers, will find a wealth of invaluable information on high-speed gas flows in this text.
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approximate Riemann solver artiﬁcial viscosity boundary treatments CFL condition CFL number chapter characteristic variables Chebyshev polynomial coefﬁcients Computational Physics concems const convergence deﬁned deﬁnition derivative differences discretization domain of dependence entropy error Euler equations exact solution example expansion fan extrema far-ﬁeld boundaries ﬁnd ﬁnite ﬁrst ﬁrst-order upwind method ﬂow ﬂuid ﬂux function ﬂux splitting ﬂux vector splitting ﬂux-corrected method Fourier series FTCS grid Harten’s inﬁnite initial conditions interpolation polynomial jump discontinuities Lax—Friedrichs method Lax—Wendroff method Leer Legendre polynomial limiter linear advection equation matrix maxima and minima methods seen minmod nonlinear stability conditions numerical methods order of accuracy polynomial series reconstruction reconstruction—evolution method Riemann problem Riemann solver Roe’s ﬁrst-order upwind samples satisﬁes scalar conservation laws second-order accurate second-order upwind method seen in Section semidiscrete shock switch speciﬁcally speed split form spurious oscillations stencil Subsection Sweby’s ﬂux-limited method Taylor series total variation upwind range condition wave speed split