A full-wave equation that describes nonlinear propagation in a heterogeneous attenuating medium is solved numerically with finite differences in the time domain (FDTD). Three-dimensional solutions of the equation are verified with water tank measurements of a commercial diagnostic ultrasound transducer and are shown to be in excellent agreement in terms of the fundamental and harmonic acoustic fields and the power spectrum at the focus. The linear and nonlinear components of the algorithm are also verified independently. In the linear nonattenuating regime solutions match results from Field II, a well established software package used in transducer modeling, to within 0.3 dB. Nonlinear plane wave propagation is shown to closely match results from the Galerkin method up to 4 times the fundamental frequency. In addition to thermoviscous attenuation we present a numerical solution of the relaxation attenuation laws that allows modeling of arbitrary frequency dependent attenuation, such as that observed in tissue. A perfectly matched layer (PML) is implemented at the boundaries with a numerical implementation that allows the PML to be used with high-order discretizations. A -78 dB reduction in the reflected amplitude is demonstrated. The numerical algorithm is used to simulate a diagnostic ultrasound pulse propagating through a histologically measured representation of human abdominal wall with spatial variation in the speed of sound, attenuation, nonlinearity, and density. An ultrasound image is created in silico using the same physical and algorithmic process used in an ultrasound scanner: a series of pulses are transmitted through heterogeneous scattering tissue and the received echoes are used in a delay-and-sum beam-forming algorithm to generate a images. The resulting harmonic image exhibits characteristic improvement in lesion boundary definition and contrast when compared with the fundamental image. We demonstrate a mechanism of harmonic image quality improvement by showing that the harmonic point spread function is less sensitive to reverberation clutter.