hypotension
发表于 2025-3-25 06:30:28
The Derivation of Conservation Lawsdynamics problem, for example flow in a tube where properties of the gas such as density and velocity are assumed to be constant across each cross section of the tube. Let x represent the distance along the tube and let . be the density of the gas at point x and time ..
Inclement
发表于 2025-3-25 07:46:12
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洞察力
发表于 2025-3-25 14:18:55
Shocks and the Hugoniot Locus eigenvalues λ.(.) <…< λ.(.) and hence linearly independent eigenvectors. We choose a particular basis for these eigenvectors, {.{.)}., usually chosen to be normalized in some manner, e.g. ∥.(itu})∥ ≡ 1.
邪恶的你
发表于 2025-3-25 18:53:58
The Riemann problem for the Euler equationst the details are messier. Instead, I will concentrate on discussing one new feature seen here, contact discontinuities, and see how we can take advantage of the linear degeneracy of one field to simplify the solution process for a general Riemann problem. Full details are available in many sources, for example , , .
附录
发表于 2025-3-25 21:15:33
978-3-7643-2723-1Springer Basel AG 1992
凶残
发表于 2025-3-26 02:59:04
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陶醉
发表于 2025-3-26 06:27:37
High Resolution Methods numerical dissipation in monotone methods. Some dissipation is obviously needed to give nonoscillatory shocks and to ensure that we converge to the vanishing viscosity solution, but monotone methods go overboard in this direction.
Asymptomatic
发表于 2025-3-26 12:08:30
Some Scalar Examplescase of gas dynamics, with gas molecules taking the place of cars. This application is discussed in much more detail in Chapter 3 of Whitham. The second example (two phase flow) shows what can happen when . is not convex.
Generosity
发表于 2025-3-26 14:24:14
Semi-discrete Methods equations in time, called the “semi-discrete equations”. We then discretize in time using any standard numerical method for systems of ordinary differential equations. This approach of reducing a PDE to a system of ODEs, to which we then apply an ODE solver, is often called the method of lines.
Irascible
发表于 2025-3-26 16:52:45
Nonlinear Stabilityas been completely successful only for scalar problems. For general systems of equations with arbitrary initial data no numerical method has been proved to be stable or convergent, although convergence results have been obtained in some special cases (. , , ).