Shock Wave: bvpT24
shock wave problem: bvpT24 | |
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Contributor: | testset of J.R. Cash |
Discipline: | fluid dynamics |
Accession: | 2013 |
Short description:
The problem describes a shock wave in a one dimension nozzle flow. The steady state Navier-Stokes equations generate a second order differential equations that is reduced to a first order system of 2 equations.
Applicable solvers:
all the solvers supported by the Test Set.
Plots of the solution <- click to generate the plots of the solution and the textual output
Mathematical description:
Consider a shock wave in a one dimension nozzle flow. The steady state Navier-Stokes equations give
where t is the normalized downstream distance from the throat, z is the normalized velocity, A(t) is the area of the nozzle at t , with
We write this problem in first order form by defining and , yielding a system of differential equations of the form
where
with
The boundary conditions are obtained from
Given its simple appearence, the BVP turns out to be a surprisingly difficult numerically. An shock develops, whose location depends on .
Singular-perturbation-type problems usually require a continuation method to solve them .For this BVP, however, many steps need to be taken.
Download:
- Fortran code: bvpT24.f
- matlab code: bvpT24.m
- R code: first order: bvpT24.R, high order: bvpT24_ho.R