Related Experiment Video
Updated: Feb 4, 2026

Fabrication, Operation and Flow Visualization in Surface-acoustic-wave-driven Acoustic-counterflow Microfluidics
Published on: August 27, 2013
A Source Term Approach for Generation of One-way Acoustic Waves in the Euler and Navier-Stokes equations
11200 E California Blvd, Pasadena, CA 91125, USA, Division of Engineering and Applied Science, California Institute of Technology.
Abstract:
We derive a volumetric source term for the Euler and Navier-Stokes equations that mimics the generation of unidirectional acoustic waves from an arbitrary smooth surface in three-dimensional space. The model is constructed as a linear combination of monopole and dipole sources in the mass, momentum, and energy equations. The singular source distribution on the surface is regularized on a computational grid by convolution with a smeared Dirac delta function. The source is implemented in the Euler equations using a Cartesian-grid finite-volume WENO scheme, and validated by comparing with analytical solution for unidirectional planar and spherical acoustic waves. Using the scheme, we emulate a spherical piezoelectric transducer and a multi-array transducer to simulate focused ultrasound fields in water. The simulated ultrasound fields show favorable agreement with previous experiments.
Related Concept Videos
Navier–Stokes Equations
Euler Equations of Motion
Euler's Equations of Motion
Electromagnetic Wave Equation
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations:...
Equations of Wave Motion
The Nernst Equation
The interconnection between standard cell potentials and various thermodynamic parameters such as the standard free energy change ΔG° and equilibrium constant K has been previously explored. For example, a redox reaction involving zinc(II) and tin(II) ions at 1 M concentration with Eºcell = +0.291 V and ΔG° = −56.2 kJ is spontaneous.

