The solution for the eikonal equation with a point-source condition has an upwind singularity at the source point as the eikonal solution behaves like a distance function at and near the source. As such, the eikonal function is not differentiable at the source so that all formally high-order numerical schemes for the eikonal equation yield first-order convergence and relatively large errors. Th...

An integral part of air quality management is knowledge of the impact of pollutant sources on ambient concentrations of particulate matter (PM). There is also a growing desire to directly use source impact estimates in health studies; however, source impacts cannot be directly measured. Several limitations are inherent in most source apportionment methods motivating the development of a novel h...

The development of a Hybrid high order Eulerian-Lagrangian algorithm to simulate shock wave interactions with particles is discussed. The Hybrid high order WENO/central finite difference scheme is assessed in three-dimensional simulations, as well as the effective use of the high order polynomials and regularization techniques in the approximation to the singular source term in the advection eq...