Abstract. We study a general approach to solving conservation laws of the form qt+f (q, x)x = 0, where the flux function f (q, x) has explicit spatial variation. Finite-volume methods are used in which the flux is discretized spatially, giving a function f i (q) over the ith grid cell and leading to a generalized Riemann problem between neighboring grid cells. A high-resolution wave-propagation algorithm is defined in which waves are based directly on a decomposition of flux differences f i (Q i ) − f i−1 (Q i−1 ) into eigenvectors of an approximate Jacobian matrix. This method is shown to be second-order accurate for smooth problems and allows the application of wave limiters to obtain sharp results on discontinuities. Balance laws qt + f (q, x)x = ψ(q, x) are also considered, in which case the source term is used to modify the flux difference before performing the wave decomposition, and an additional term is derived that must also be included to obtain full accuracy. This method is particularly useful for quasi-steady problems close to steady state.

The collision of a solitary wave, travelling over a horizontal bed, with a vertical wall is investigated using a boundary-integral method to compute the potential fluid flow described by the Euler equations. We concentrate on reporting new results for that part of the motion when the wave is near the wall. The wall residence time, i.e. the time the wave crest remains attached to the wall, is introduced. It is shown that the wall residence time provides an unambiguous characterization of the phase shift incurred during reflection for waves of both small and large amplitude. Numerically computed attachment and detachment times and amplitudes are compared with asymptotic formulae developed using the perturbation results of Su & Mirie (1980). Other features of the flow, including the maximum run-up and the instantaneous wall force, are also presented. The numerically determined residence times are in good agreement with measurements taken from a cine film of solitary wave reflection experiments conducted by Maxworthy (1976).

In this paper, we theoretically investigate the mechanism of polarization in wide-bandgap semiconductor radiation detectors under high-flux x-ray irradiation. Our general mathematical model of the defect structure within the bandgap is a system of balance laws based on carrier transport and defect transition rates, coupled together with the Poisson equation for the electric potential. The dynamical system is self-consistently evolved in time using a high-resolution wave propagation numerical algorithm. Through simulation, we identify and present a sequence of dynamics that determines a critical flux of photons above which polarization effects dominate. Using the experience gained through numerical simulation of the full set of equations, we derive a reduced system of conservation laws that describe the dominant dynamics. A multiple scale perturbation analysis of the reduced system is shown to yield an analytical dependence of the maximum sustainable flux on key material, detector, and operating parameters. The predicted dependencies are validated for 16ϫ 16 pixel CdZnTe monolithic detector arrays subjected to a high-flux 120 kVp x-ray source.

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