About Wave2500™
Wave2500™ is a standalone computer software program for computational
ultrasonics for problems that are 3Daxisymmetric  in cylindrical coordinates.
It was produced to bring numerical simulation to the ultrasound engineering
community. This page provides some basic information about Wave2500™ including
a general Program Overview, Hardware/Software/Memory
Requirements, and a brief description of the Wave Equation that
is being simulated.
Program Overview
Wave2500™ is a standalone software package for computational ultrasonics.
It operates by solving the threedimensional (3D) acoustic (viscoelastic) axisymmetric
wave equation based on a method of finite differences. The solution is computationally
intensive. However, thanks to the ever increasing power and speed of computer
hardware, it is now possible to bring such software packages to the desktop
and personal computer of the ultrasound engineer and researcher.
Wave2500™ allows the user to compute the full viscoelastic wave solution
(both longitudinal and shear displacements) in an arbitrary threedimensional
(3D) object that is axisymmetric (that is, does not have any changes in materials
as a function of the angle phi around the axis, when the radius, r, and height,
z, are constant), subjected to userspecified acoustic sources (which themselves
must also be axisymmetric; that is either circular disks or annuli). The program,
besides simulating the complete spatial and timedependent acoustic solution,
allows the user to simulate ultrasound measurements in a variety of source
and receiver configurations. Wave2500™ will prove useful to researchers
and applications engineers in such diverse fields as nondestructive testing,
materials evaluation, medical imaging and biological tissue characterization.
The software is useful also in basic mechanistic studies and for academic applications.
With Wave2500™ the user can compute solutions (e.g., scattered and reflected
waveforms) to virtually an unlimited variety of distinct physical problems
without ever leaving the computer keyboard.
Wave2500™ provides solutions to a broad range of 3D axisymmetric ultrasound
problems. The program allows the user to specify an arbitrary object which
is ultrasonically interrogated. The object is specified in a "PCX" (2D) image
file. The objects are by definition cylindrical (or annular); however owing
to the assumed axisymmetric property, a 2D image is sufficient to describe
the entire 3D object; that is, any crosssection through the cylinder
axis  as represented by a 2D image file  is sufficient to describe the
object. Thus, for those users already familiar with Wave2000® (our 2D
ultrasound simulation software), the similarity of the two programs will be
apparent in terms of the 2D image representing the object; however, the equations
for Wave2500™ ensure that the simulated data obtained will actually represent
propagation of ultrasound in the 3D (cylindrical and axisymmetric) object.
"PCX" is a "triedand true" graphics file format which includes within it
absolute size information, a useful feature for the ultrasound simulations.
The image data or object is composed of individual pixels which can have 1
of 256 gray levels (0255). Each pixel value represents a physical material
(e.g., water, steel, etc.) that is set by the user. Gray level 255 is reserved
by Wave2500™ to denote void (i.e., vacuum). There is thus a vast variety
of 3D axisymmetric structures in which ultrasound propagation can be simulated
using Wave2500™.
The 2D object or image representing the crosssection of the 3D object to
be simulated can be generated either internally using Wave2500 "Geometry" routines
or externally using any graphics program (commercial or "inhouse") which can
output files in 8 bit monochrome "PCX" format. Additionally, the image may
be obtained from various scan modalities, for example CT or MRI slice data,
which has been converted to "PCX" format. Usually, a segmentation algorithm
of some kind would be necessary to properly associate various regions of the
image with a particular material (i.e., grey level).
The attractiveness of Wave2500™ is that it is very easy to generate
solutions to a wide variety of 3D axisymmetric ultrasound problems within a
simple graphical interface. The user has access to features designed to mimic
reasonably closely many practical situations. For example, there are source
and receiver configurations that the ultrasound engineer will notice are similar
to real ultrasound experimental configurations, for example the use of signals
that characterize many transducer generated waveforms. As one application, Wave2500™ may
be useful for analyzing ultrasound propagation in cladded rods (e.g., a plastic
rod surrounded by an aluminum sheath). In addition, the software could be used
to explore the use of circumferential transducer sources (i.e., sources which
wrap around a rod).
Wave2500™ has the potential to generate new insights and approaches
to many problems in ultrasonics. For the first time, the user has the capability
to "experiment" to his or her heart's content, without turning on a pulserreceiver
or connecting a "BNC" cable. Indeed, the simulations can "run" while the user
is word processing a document or analyzing data from an earlier simulation.
The computer can work "around the clock" (for example, by using the "Multibatch
feature") computing solutions to problems that are difficult to perform in
the laboratory or the field, but the results of the simulations can provide
important understanding and knowledge for future experiments or for data already
collected.
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Hardware, Software and Memory Requirements
Wave2500™ is designed to run on any PC that has the Windows XP, Vista, 7 or 8 operating systems installed. Minimum hardware requirements are
extremely modest (for example 15 megabytes free hard disk space and 128 megabytes
memory), although we recommend 1 GB or more memory for handling the larger
simulation models. (Detailed information on memory requirements can be found
in the 'Algorithm' topic of the Wave2500™ User Guide Section of
the Help file.) Minimum graphics requirements are 256 color VGA and a compatible
mouse, but of course most systems will have hardware characteristics much higher
than these minimums. As noted, Wave2500™ operates best with as much
RAM memory as possible, which allows problems of increasingly larger size to
be accommodated and avoids the need for virtual (disk) memory to be used. Note
also that Wave2500™ supports multiprocessor systems, that allows
the program to potentially speedup the execution of the program. This is most
effective for "large" objects; experimentation by the user will determine when
multiprocessors can lead to faster execution times. The multiprocessors can
be either actual multiproccessor systems, or multicore processors, or both.
Wave2500™ is a "memoryhungry" program; this is simply the nature of
the acoustic problem which is being simulated. To aid the user in assessing
the memory requirements for a particular simulation model, we can provide the
following approximate relationships.
Because of the axisymmetric nature of the problem, the memory requirements
can be computed based on the "size" of the 2D crosssection, as follows: The
simplest approach for approximating memory needed is to multiply the number
of finite difference grid elements, N, by 30; this is the amount of memory
required in bytes (plus some additional "fixed" program overhead which can
usually be neglected in comparison to the 30 x N quantity). As an example,
if an object image crosssection is 3 cm x 4 cm and the pixel resolution ("Pixels/mm")
is 10 pixels/mm, the number of pixels in this image will be 300 x 400 = 120,000
pixels. Now if we assume that the finite difference grid elements generated
by Wave2500™ are coincident with the number of image pixels (i.e., Grid/Pixel
= 1), then the memory required is 30 x N = 30 x 120,000 = 3.4 megabytes.
Another perspective on memory requirements can be gained by determining the
memory needed as a function of object (crosssection) size in terms of wavelengths.
In the example above, it was assumed the the grid size was coincident with
object image pixel size, i.e., both were 0.1 mm square (10 pixels/mm). For
the case of a problem in which the minimum wavelength is about 1 mm, this 0.1
mm size for the finite difference grid element should provide a reasonably
accurate solution. We may extend this reasoning for a more generic assessment
of memory requirements as follows. Assuming that we would like to have a grid
element dimension 10 times less than the minimum wavelength, then that implies
that 100 x 30 = 3000 bytes for a square object 1 wavelength on a side. If one
has a square object which is 10 wavelengths on a side, then using the same
relative grid dimensions, Wave2500™ would require about 10,000 x 30 = 293 kilobytes
of memory. One may also extend this approximation to any number of (minimum)
wavelengths to evaluate memory requirements. Assuming a rectangular object
Q wavelengths by R wavelengths in overall dimensions, and again assuming 10
grid elements per wavelength, then the memory required for this model is approximately
30 x 100 x Q x R = 2.93 Q x R kilobytes. It is useful to also point out that
the minimum wavelength is inversely proportional to the frequency of the source
waveform. Therefore, if a simulation with a 1 MHz source waveform requires
1 megabyte of memory, then changing to a source waveform operating at 2 MHz
will generally require four times as much memory, or in this case 4 megabytes,
to be used. (This assumes that the same size object is used in both cases.)
Thus the user may want to carry out as many of his or her simulations as possible
with relatively low frequency sources, in order to reduce computational overhead.
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Wave Equation
The specific viscoelastic wave equation that is simulated in a Wave2500™ simulation
is given by:
rho {d^2 ur / dt^2} = (lambda + (phi2/3 eta) d/dt + 2 mu + 2 eta d/dt) d/dr
{(1/r) d/dr(rur)} + (mu + eta d/dt) d^2 ur/dz^2 + (lambda + (phi2/3 eta) d/dt)
+ mu + eta d/dt) d^2uz/dzdr
rho {d^2 uz / dt^2} = (lambda + (phi2/3 eta) d/dt + mu + eta d/dt) (1/r)
d/dr {dur/dz)} + (lambda + (phi2/3 eta) d/dt + 2 mu + 2 eta d/dt) d^2 uz/dz^2
+ (mu + eta d/dt)(1/r) d/dr (rduz/dr)
In the above equations, which applies in a cylindrical isotropic elastic region,
rho = material density [kg/m^3],
lambda = first Lame constant [N/m^2],
mu = second Lame constant [N/m^2],
eta = shear viscosity [Ns/m^2],
phi = bulk viscosity [Ns/m^2],
d denotes the partial differential operator,
t = time [s],
and
ur is the radial displacement and uz is the displacement in the z direction,
where the zaxis is the cylinder axis. Note that ur and uz are functions of
(r,z), and independent of the angle phi around the axis (based on the assumed
axisymmetric properties of the object and sources).
Wave2500™ solves the above equation set within each homogeneous grid
element of the object, and computes (and displays) the (magnitude of the) displacement
vector [ur uz] at the intersection of 4 grid elements at each time step of
the simulation.
Wave2500™ does not implement "raytracing" or other "nongeneral" methods
in simulating ultrasound measurements. Rather, it is a comprehensive engineering
software package designed to compute the full and accurate solution to
practically any 3D axisymmetric ultrasonic problem. Wave2500™ simulates
data that you would measure on the lab bench or in the field. In addition,
it has an easy to use graphical user interface allowing you to begin simulating
complex ultrasound problems in a matter of minutes after receiving your Wave2500™ software.
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For features available in Wave2500™, you can look at Wave2500 page. For additional information, you may want to review several of our Wave2500
Examples. In addition you can download the program and obtain a free
time limited license for program evaluation by registering
with us and logging in. Information on pricing is
also available. Please Contact Us to discuss your
intended application(s) or for any other additional information you would
like to have on Wave2500™.
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