README.md


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# couscous

## centered scheme for linear acoustic equations in heterogeneous medium

a centered solver for the solution of nonconservative hyperbolic
systems, such as the acoustic equations derived in [1]. the main
file here implements the primitive centered scheme (price) from [2].

## example

this is a benchmark taken from [1]. we note that this scheme is much more diffusive 
than godunov-type schemes that utilize eigenstructure information to approximate
the numerical flux. in this example, we use 500 elements to obtain results with
similar accuracy to the wave propagation scheme in [1] with 100 elements.

![res26](https://github.com/zgxn/acoustic/blob/master/img/res26.png "image")

## references

[1] leveque, r.j. wave propagation algorithms for multidimensional hyperbolic
systems, journal of computational physics 131, 327-353, 1997.

[2] toro, e.f., siviglia, a. price: primitive centered schemes for hyperbolic
systems, international journal for numerical methods in fluids 42, 1263-1291,
2003.