Systems and methods of conducting numerical simulation of an underwater explosion

Characteristics of a blast source and a FEA model representing a surrounding fluid domain are defined. One layer of new border nodes and elements are created outside of the fluid domain's original outer boundary formed by the original border elements. Each new border element/node is associated with one of the original border elements/nodes as corresponding master element/node. At each time step of a time-marching simulation of an underwater explosion, simulated fluid behaviors are computed for all but the new border elements. The computed fluid behaviors of each original border element are saved into a corresponding lookup table configured to store the computed fluid behaviors for a predefined number of time steps in a first-in-first-out manner. Simulated fluid behaviors of each new border element are determined by interpolating, with the calculated blast wave propagation time from the master element, the stored fluid behaviors in the corresponding master element's lookup table.

FIELD

The present invention generally relates to methods, systems and software product used in computer-aided engineering analysis, more particularly to method of conducting efficient numerical simulation of underwater explosion.

BACKGROUND

Finite element analysis (FEA) is a computer implemented method using a numerical technique for finding approximate solutions of partial differential equations representing complex systems such as three-dimensional non-linear structural design and analysis. The FEA originated from the need for solving complex elasticity and structural analysis problems in civil and aeronautical engineering. With the advance of the computer technology, FEA has become a vital tool for assisting engineers and scientists to make decisions in improving structural design (e.g., automobile, airplane, etc.). When applying FEA in solving a physical problem or event in time domain, it is referred to as a time-marching simulation. In general, a time-marching simulation comprises a number of solution cycles. A FEA result or solution is obtained at each solution cycle as a snap-shot of the total simulation at a particular time.

As popularity of the FEA grows, the use of FEA has been adapted to simulate more complex physical phenomena, for example, fluid behaviors due to an underwater explosion. To numerically simulate such behaviors, a technique referred to as Arbitrary Lagrangian-Eulerian (ALE) based finite element analysis (FEA) method is preferably used.

A common practice for conducting numerical simulation of an underwater explosion using the ALE based FEA method is to only model a limited portion of a fluid domain due to limitation of computing resources. Element stress wave originated inside the fluid domain, as result of the blast, would get reflected at the FEA model's boundary. When the boundary is modeled relatively too close to the blast source, such stress wave reflections cause incorrect simulation results. Prior art approaches to correct this problem/shortcoming is either to enlarge the FEA model or to apply artificial normal and shear stresses at the FEA model's boundary to compensate effects of such stress wave reflections. Although the prior art approaches may reduce some effects, it cannot eliminate them. Furthermore, the prior art approaches require many ad hoc techniques that are not easy to practice.

It would, therefore, be desirable to have improved systems and methods of conducting time-marching numerical simulation of underwater explosion to avoid the aforementioned shortcomings.

BRIEF SUMMARY

This section is for the purpose of summarizing some aspects of the present invention and to briefly introduce some preferred embodiments. Simplifications or omissions in this section as well as in the abstract and the title herein may be made to avoid obscuring the purpose of the section. Such simplifications or omissions are not intended to limit the scope of the present invention.

Systems and methods of conducting a time-marching numerical simulation of an underwater explosion are disclosed. According to one aspect, characteristics of an underwater blast source and a finite element analysis (FEA) model containing a number of nodes connected by a number of finite elements representing a fluid domain surrounding the blast source are defined and received in a computer system. An Arbitrary Lagrangian-Eulerian (ALE) based finite element analysis (FEA) application module is installed in the computer system. The FEA model may represent only a portion of the fluid domain due to geometric symmetry.

Nodes and elements located on the original outer boundary of the fluid domain are identified as original border nodes and origin border elements, respectively. One extra layer of new border nodes and new border elements are then created outside of the original outer boundary of the fluid domain between the original border nodes and the new border nodes. The new border elements are so sized that none of the new border elements is smaller than the smallest one of the original border elements. Each new border element/node is associated with one of the original border elements/nodes as corresponding master element/node.

Simulated fluid behaviors as a result of an underwater explosion originated from the blast source are obtained in a time-marching numerical simulation using the modified FEA model for a predetermined duration in a number of time steps.

At each time step of the time-marching simulation, simulated fluid behaviors are computed for all but the new border elements with the ALE based FEA module. The computed fluid behaviors of the original border elements are then saved into respective lookup tables with one table per each original border element. Each lookup buffer is configured to store the computed fluid behaviors for a predefined number of time steps in a first-in-first-out (FIFO) manner.

Simulated fluid behaviors of each new border element are determined by interpolating, with the calculated blast wave propagation time from the corresponding master element to each new border element, the stored fluid behaviors in the corresponding master element's lookup buffer.

DETAILED DESCRIPTION

Referring first toFIGS. 1A-1B, it is collectively shown a flowchart illustrating an example process100of conducting a time-marching numerical simulation an underwater explosion, according to an embodiment of the present invention. Process100can be implemented in software (e.g., an ALE based FEA application module) and is preferably understood with other figures.

FIG. 2depicts an elevation view showing a blast source (shown as solid dot) with blast waves (shown in dotted circles) propagating through a fluid domain in an example underwater explosion. Numerical simulation of such an underwater explosion may be conducted using one embodiment of the present invention.

Process100starts by receiving characteristics of an underwater blast source and a finite element analysis (FEA) model representing a fluid domain surrounding the blast source in a computer system (e.g., computer system1000inFIG. 10) having an arbitrary Lagrangian-Eulerian (ALE) based FEA application module installed thereon at action102.

The FEA model contains a number of nodes connected by a number of finite elements. A first example FEA model310with a blast source312is shown inFIG. 3A. Alternatively, due to geometric symmetry, second and third FEA models320-330with blast sources322-332are shown inFIG. 3BandFIG. 3C, respectively. For illustration simplicity, these FEA models310-330are drawn in two-dimension. For those having ordinary skill in the art would know that the FEA model can be drawn in three-dimension.

Example finite elements may be used in the example FEA model are shown inFIGS. 4A-4B: 4-node quadrilateral element410in two-dimension and 8-node hexahedral finite element420in three-dimension.

The characteristics of an underwater blast source include at least a location of the blast source (e.g., blast sources313,322,332inFIGS. 3A-3C) and a blast wave velocity and pressure.FIG. 5is an X-Y plot showing an exemplary curve of pressure504versus time502of the blast pressure500due to an explosion at a particular location in accordance with one embodiment of the present invention. Blast pressure500is equal to an initial ambient pressure P0520(e.g., atmosphere pressure in an open space) when time is at zero or t0, and stays constant until time t1. Blast pressure500then jumps to peak pressure P1512, which corresponds to the moment when the blast wave reaches the particular location. The magnitude of the peak pressure P1512is a function of distance between the particular location and the blast source, and the mass of the blast source. Blast pressure500drops off thereafter. Depending upon types of transmission medium (e.g., air, water) and the particular location, the trailing portion514of the blast pressure500can decay in various forms.

Referring back to process100, at action104, those nodes and finite elements located on the fluid domain's original outer boundary (i.e., the border the FEA model) are identified as original border nodes and original border elements, respectively.FIG. 6shows an example FEA model600having original border nodes612(solid dots) and original border elements614(lighter shaded elements). Next, at action106, one extra layer of new border nodes622are created to form one layer of new border elements624(darker shaded elements) between the original border nodes612and the new border nodes622. The new border elements624are so sized that none of the new border elements624is smaller than the smallest one of the original border elements614.

At action108, each new border element is associated with the closest neighboring original border element as its master element and each new border node is associated with the closest one of the original border nodes as its master node.

Example of the node associations are shown inFIG. 7A, new border node702is associated with a first original border node712as its master node. A second original border node714is the master node for three new border nodes704a-704c. Further, a third original border node716is the master node for new border node706.FIG. 7Bshows example element associations. A first original border element732is the master element of new border element722. The second original border element734is the master element for three new border elements724a-724c. The third original border element736is the master element for new border element726.

Then at action110, simulated fluid behaviors as a result of an underwater explosion originated from the blast source are obtained by conducting a time-marching simulation using the modified FEA model (i.e., the original FEA model with an extra layer of new border elements) for a predetermined duration in a number of time steps. The duration can be predetermined by a user or by a feature in the ALE based FEA application module. In one embodiment, a user can set the duration of simulation by inputting a value (e.g., 0.1 second, 0.5 second. etc.). In another embodiment, the application module can have a default value (e.g., 0.25 second, 0.75 second, etc.). In yet another embodiment, the application module can have an option to detect a particular end condition (e.g., blast wave has decayed below a threshold, etc.).

Next, at action112, to avoid blast wave (stress wave) reflections from the original outer boundary at each time, the following operations/actions are performed by the ALE based FEA module. At action112a, simulated fluid behaviors are computed for all but the new border elements. In other words, all of the finite elements in the original FEA model are treated like interior finite elements thereby no blast wave/stress wave reflections would occur. The simulated fluid behaviors include at least the element stresses, the element strains and nodal velocities for each finite element. For finite elements having non-linear material properties, the simulated fluid behaviors further include element history variables for reconstruct non-linear events (e.g., loading and unloading paths).

At action112b, the computed simulated fluid behaviors of the original border elements and nodes are saved into respective lookup tables with one table per original border element. Each table is configured to store simulated fluid behaviors for a predefined number of time steps in a first-in-first-out (FIFO) manner.FIG. 8shows an example data structure of a lookup table. Fluid behaviors in form of element stresses, element strains, nodal velocities, and optional element history variables are stored for a predefined number of time steps (e.g., steps t, t-Δt, t-2Δt, . . . , t-nΔt). “t” represents the current simulation time, while Δt represents the size of each time step. “n” is a whole number. In this example, the predefined number is “n+1”.

The FIFO table shown inFIG. 9comprises a slide window of time of the duration of the time-marching simulation. The size of the lookup table depends upon the predefined number of time steps, which can be determined by certain features in the ALE based FEA application module (e.g., default value, user-defined value, etc.). For those having ordinary skill in the art would know that the sliding window holds computed results for a predefined number of time steps that moves forward with the simulation time (t). In other words, as the simulation marches forward in time, the latest computed results are stored into the lookup table, while the oldest saved results are removed (i.e., first-in-first-out).

At action112c, the blast wave propagation time from the corresponding master element to each new border element is calculated. One example scheme is to divide the distance between these two elements (i.e., master and each new border element) by speed of the sound in the fluid. Since the master element and each new border element can be located not aligned with the blast source, the distance calculation may include a consideration of the relative angle between the blast wave and the direction of the master element.

Finally, at action112d, simulated fluid behaviors of each new border elements are determined by interpolating, with the calculated blast wave propagation time, the previously-stored simulated fluid behaviors of the corresponding master element's lookup table.

According to one aspect, the present invention is directed towards one or more computer systems capable of carrying out the functionality described herein. An example of a computer system1000is shown inFIG. 10. The computer system1000includes one or more processors, such as processor1004. The processor1004is connected to a computer system internal communication bus1002. Various software embodiments are described in terms of this exemplary computer system. After reading this description, it will become apparent to a person skilled in the relevant art(s) how to implement the invention using other computer systems and/or computer architectures.

Computer system1000also includes a main memory1008, preferably random access memory (RAM), and may also include a secondary memory1010. The secondary memory1010may include, for example, one or more hard disk drives1012and/or one or more removable storage drives1014, representing a floppy disk drive, a magnetic tape drive, an optical disk drive, flash memory card reader, etc. The removable storage drive1014reads from and/or writes to a removable storage unit1018in a well-known manner. Removable storage unit1018, represents a floppy disk, magnetic tape, optical disk, flash memory, etc. which is read by and written to by removable storage drive1014. As will be appreciated, the removable storage unit1018includes a computer recordable storage medium having stored therein computer software and/or data.

In alternative embodiments, secondary memory1010may include other similar means for allowing computer programs or other instructions to be loaded into computer system1000. Such means may include, for example, a removable storage unit1022and an interface1020. Examples of such may include a program cartridge and cartridge interface (such as that found in video game devices), a removable memory chip (such as an Erasable Programmable Read-Only Memory (EPROM), Universal Serial Bus (USB) flash memory, or PROM) and associated socket, and other removable storage units1022and interfaces1020which allow software and data to be transferred from the removable storage unit1022to computer system1000. In general, Computer system1000is controlled and coordinated by operating system (OS) software, which performs tasks such as process scheduling, memory management, networking and I/O services.

There may also be a communications interface1024connecting to the bus1002. Communications interface1024allows software and data to be transferred between computer system1000and external devices. Examples of communications interface1024may include a modem, a network interface (such as an Ethernet card), a communications port, a Personal Computer Memory Card International Association (PCMCIA) slot and card, etc.

The computer1000communicates with other computing devices over a data network based on a special set of rules (i.e., a protocol). One of the common protocols is TCP/IP (Transmission Control Protocol/Internet Protocol) commonly used in the Internet. In general, the communication interface1024manages the assembling of a data file into smaller packets that are transmitted over the data network or reassembles received packets into the original data file. In addition, the communication interface1024handles the address part of each packet so that it gets to the right destination or intercepts packets destined for the computer1000.

In this document, the terms “computer program medium” and “computer recordable medium” are used to generally refer to media such as removable storage drive1014, and/or a hard disk installed in hard disk drive1012. These computer program products are means for providing software to computer system1000. The invention is directed to such computer program products.

Computer programs (also called computer control logic) are stored as application modules1006in main memory1008and/or secondary memory1010. Computer programs may also be received via communications interface1024. Such computer programs, when executed, enable the computer system1000to perform the features of the present invention as discussed herein. In particular, the computer programs, when executed, enable the processor1004to perform features of the present invention. Accordingly, such computer programs represent controllers of the computer system1000.

In an embodiment where the invention is implemented using software, the software may be stored in a computer program product and loaded into computer system1000using removable storage drive1014, hard drive1012, or communications interface1024. The application module1006, when executed by the processor1004, causes the processor1004to perform the functions of the invention as described herein.

The main memory1008may be loaded with one or more application modules1006(e.g., finite element analysis application module based on ALE technique) that can be executed by one or more processors1004with or without a user input through the I/O interface1030to achieve desired tasks. In operation, when at least one processor1004executes one of the application modules1006, the results are computed and stored in the secondary memory1010(i.e., hard disk drive1012). The result and/or status of the ALE based finite element analysis (e.g., fluid behaviors) is reported to the user via the I/O interface1030either in a text or in a graphical representation to a monitor coupled to the computer.

Although the present invention has been described with reference to specific embodiments thereof, these embodiments are merely illustrative, and not restrictive of, the present invention. Various modifications or changes to the specifically disclosed exemplary embodiments will be suggested to persons skilled in the art. For example, whereas the time step size (Δt) has been shown as a constant. Non-constant time step size can also be used to achieve the same. In summary, the scope of the invention should not be restricted to the specific exemplary embodiments disclosed herein, and all modifications that are readily suggested to those of ordinary skill in the art should be included within the spirit and purview of this application and scope of the appended claims.