## 1 Introduction  
Understanding the structure of blast waves and the dynamics of their interactions with structures is key for mitigation and safety. The formation and propagation of these shock waves is a highly nonlinear dynamic process; thus, prediction of the incident waveforms and their corresponding blast overpressure and impulsive loads for a given scenario can be difficult. It is common for various government, military, and scientific institutions to prescribe criterion for safety from blast effects in terms of \"\(K\) factors\":  
\[K=R/W^{1/3} \tag{1}\]  
Here, \(R\) is the distance from the explosive source and \(W\) is the net explosive (TNT equivalent) weight. Allowable exposure for personnel, nearby structures, and withdrawal distances can be given in terms of these \(K\) factors, which have been empirically correlated to values of incident overpressure and impulse. A figure regularly encountered in explosive safety documentation is the K328 criterion, often referred to as the \"Public Withdrawal Distance\"; calculated using units of ft/lb\({}^{1/3}\) this corresponds to a peak incident overpressure of 0.0655 psi, (0.4516 kPa) and is said to be a condition under which there is no probability of harm. Different safety guidelines have different requirements for personnel, but they are very commonly given in terms of these \(K\) factors. The empirical nexus of \(K\) factor correlation appears to be the work of [PERSON] [1,2]. The original data came from quite large (5, 20, 100, and 500 ton) hemispherical TNT events. Instrumentation at various distances measured arrival time, peak overpressure, and the duration of the positive pressure phase and the positive impulse. This same data set was later reinterpreted and extrapolated to include reflected pressures/impulse and shock velocities by [PERSON] and [PERSON] [3]. It is these fits which became the basis for more widespread application, and thus the empirical equations are often referred to as Kingery-Bulmans (KB) curves. [PERSON] [4] provides a good overview of this history, along with improved equations fitting the same data. More recent fits by [PERSON] et al. [5] claim to further simplify the curves with the same accuracy. There is definite uncertainly in the accuracy of the KB curves and other analytic and empirical tools for predicting blast overpressure in a given case. [PERSON] et al. [6; 7; 8] have investigated the structure of blast waves and their parameters for scaling and decay, including variations in explosive type, weight, and configuration on the resulting incident pulses. A recent review of analytical and empirical prediction methods by [PERSON] et al. [9] shows a very large spread in the predicted blast overpressures and wave structures from various accepted sources. Recent repeated blast measurements from [PERSON] et al. [10] show large variability in the measured results from what are ostensibly the same experiments. The recent experiment of [PERSON] et al. [11] provides more data and KB comparisons and variances for relatively nearby (2-5 m) and relatively small (100-400 g) explosives. In a review of the experimental literature vs. KB predictions, [PERSON] et al. [12] state that the variation in experimental predictions is so large in nominally similar experiments that there is a valid question as to whether blast phenomena are inherently deterministic, or whether they should be viewed as fundamentally stochastic processes. Under this lens, KB and others may be viewed as useful only at predicting the order of magnitude of blast effects. The question arises: can direct physics-based calculation of blast wave parameters provide more detailed and accurate predictions for a given case of interest? The classical analytical result for the prediction of the evolution of a very strong explosion is the so-called Taylor-von Neumann-Sedov solution [13; 14; 15; 16]. This applies only to spherical (1D) blasts and is derived under assumptions (point source, zero ambient pressure) that leave it applicable only for intermediate distances.