AbstractIt is commonly (but erroneously) assumed that the best way to treat upstream boundaries for hyperbolic equations is to let the numerical value be equal to the imposed value. What is erroneous in this assumption is that it ignores the presence of spurious numerical solutions which may have originated inside of the computational domain and which may be present near the boundary. Such spurious solutions are characterized by short wavelength spatial oscillations, with a group velocity, which is opposed to the direction of flow and are therefore moving as "packets" toward the boundary. They are reflected by the "standard" treatment whereas a better numerical treatment of the boundary should attempt to absorb them. This paper describes two methods for the modified numerical treatment of upstream boundaries of hyperbolic equations, which are effective in absorbing those purious solutions with a remainder which decreases as O (r-~J) and 0~~VA"-) respectively, where _17L is the frequency and h is the mesh size.
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