The behavior of nonpremixed edge flames to low and high strains in a wedge-shaped region are simulated and studied in detail. The chemistry is modeled by a one-step mechanism and transport by constant coefficient Fickian diffusion, as a qualitative model describing the physical mechanisms in the thermochemistry of combustion of hydrocarbon fuels. The reactive zero-Mach-number Navier-Stokes equations are used to describe the flow, both in a thermodiffusive regime (constant density) and a hydrodynamically-coupled regime (variable density). This configuration is an adaptation of the experimental opposed inclined jet geometry long used at the University of Southern California, but made stationary by the addition of a sink at the apex of the wedge. This crucial modification enables the stable presence of stationary edge flames, and it allows the study of advancing and retreating edge flames in the low and high strain regimes. The dependence of the edge flames speed on strain rate, stoichiometry, and Lewis numbers is discussed and compared to previous studies. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.