SPH shell particle boundary condition processing method for underwater contact explosion

Abstract

The invention relates to an underwater contact explosion-oriented SPH shell particle boundary condition processing method. According to the SPH shell particle boundary condition processing method for underwater contact explosion, the penetration process of particles is divided into three stages: when fluid particles do not penetrate through a wall surface, when the distance between the fluid particles and the wall surface of a shell model reaches a critical value, and when the fluid particles penetrate through the wall surface. When the fluid particles i do not penetrate through the wall surface, a spatial repulsion model proposed by Monaghan and the like is adopted; when fluid particles i penetrate through the wall surface, a repulsive force-restoring force coupling model is constructed. In order to further improve the stability, a viscous damping force model is introduced, and the total acting force Ftol is equal to Frep + Frett + Fvis. According to the processing method, the boundary control capability is effectively enhanced while the ULSPH advantages are reserved, and the numerical stability and physical accuracy of solid-liquid interaction in shell particle and fluid particle coupling simulation are improved.

Description

Technical Field

[0001] This invention relates to the field of fluid-structure interaction technology for underwater contact explosions, and in particular to a method for handling SPH shell particle boundary conditions for underwater contact explosions. Background Technology

[0002] In fluid-structure interaction (FSI) simulations of smoothed particle hydrodynamics (SPH), boundary treatment remains a key challenge affecting computational accuracy and stability. Particularly in multiphysics scenarios involving shell structures and free-surface fluid coupling, fluid particle penetration through shell boundaries and non-physical oscillations near the interface have become significant bottlenecks restricting the engineering applications of SPH.

[0003] The core contradiction stems from the mathematical limitations of traditional boundary models: the fluid-structure interaction conditions based on the repulsive forces between boundary particles are constrained by the CFL condition and are difficult to resist momentum penetration under high-speed impact conditions; at the same time, due to the special properties of the single-layer particles in the shell model, the lack of a mechanism for viscous dissipation in the SPH boundary layer leads to a core truncation effect, causing errors in the calculation of near-wall shear stress. Furthermore, under the condition of a lack of consistency near the boundary, particles near the interface are prone to numerical vibration, ultimately leading to computational instability of the fluid or solid.

[0004] For example, in traditional meshless Lagrangian particle methods (such as ULSPH), fluid particles may penetrate solid boundary elements, such as shell structures, during computation due to inertia, inaccurate boundary treatment, or the kernel function's support domain crossing the boundary. This penetration not only disrupts physical boundary conditions but also leads to the mistaken inclusion of penetrating particles as particles on the other side of the shell element during neighborhood searches. This results in severe errors in local pressure, velocity, and stress fields, potentially causing non-physical oscillations and energy non-conservation problems. Summary of the Invention

[0005] To address the shortcomings of existing production technologies, this applicant provides a method for handling SPH shell particle boundary conditions in underwater contact explosions. This method employs a three-stage mechanical response mechanism to divide the particle penetration process into three stages, constructing a "repulsive-restorative force coupling model." While retaining the advantages of ULSPH, it effectively enhances boundary control capabilities and improves the numerical stability and physical accuracy of the solid-liquid interaction region in the simulation of shell particle and fluid particle coupling in underwater contact explosion simulations.

[0006] The technical solution adopted in this invention is as follows:

[0007] A method for handling particle boundary conditions in an underwater contact explosion (SPH) shell includes: dividing the particle penetration process into three stages: when the fluid particle has not penetrated the wall, when the distance between the fluid particle and the shell model wall reaches a critical value, and when the fluid particle penetrates the wall.

[0008] In the first stage, when fluid particle i has not penetrated the wall: using the spatial repulsion model proposed by Monaghan et al., the boundary repulsion F based on displacement is... rep The nonlinear power function model is expressed as formula (1).

[0009]

[0010] Where A is the repulsive force coefficient, controlling the magnitude of the repulsive force; d is the distance from the current particle to the boundary; d0 is the range of action of the repulsive force; n is the exponential coefficient; n is the boundary normal direction, pointing towards the fluid region; at this time, the total force F tol =F rep .

[0011] When the distance between fluid particle i and the shell model wall reaches a critical value in the second stage: d = 0 in formula (1), then formula (1) simplifies to formula (2).

[0012] F rep =An,d=0 (2),

[0013] Where A is the repulsion coefficient, controlling the magnitude of the repulsion force; n is the boundary normal direction, pointing towards the fluid region; at this time, the total force F tol =F rep .

[0014] In the third stage, when fluid particle i penetrates the wall: a "repulsive force-restoring force coupling model" is constructed, then the restoring force F ret The calculation expression is formula (3).

[0015] F ret =-kdV i (3),

[0016] Where k is the recovery coefficient, in N / m 4 ;d is the vector distance from the point of penetration into the boundary, pointing outwards from the boundary surface; V i Let F be the volume of the fluid particle; then the total force F tol The calculation formula is formula (4).

[0017] F tol =F rep +F ret (4).

[0018] Preferably, when fluid particle i penetrates the wall, the boundary repulsion force F rep It is a fixed value, with a value of An, where A is the repulsion coefficient, which controls the magnitude of the repulsion; n is the boundary normal direction, pointing towards the fluid region.

[0019] Preferably, d0 in formula (1) is taken as the nuclear radius h. When a particle enters this range, the repulsive force begins to take effect.

[0020] Preferably, the exponential coefficient n in formula (1) takes a value range of 1-4.

[0021] More preferably, the exponential coefficient n in formula (1) is 2.

[0022] Preferably, a viscous damping force model based on the velocity difference between fluid particle i and boundary shell model particle j is constructed, then the viscous damping force F vis The calculation formula is formula (5).

[0023]

[0024] Among them, v ij V is the relative velocity between fluid particle i and boundary shell model particle j; j Let r be the volume of the particle in the boundary shell model. ij It represents the relative position of fluid particle i and boundary shell model particle j; μ art ε is the viscous damping coefficient, controlling the dissipation intensity; N is the total number of neighboring particles of particle i, and ε is a finite quantity to prevent the denominator in formula (5) from being 0; v ij ·r ij This represents the relative motion component of the particle in the normal direction, and the direction of the force is always in the opposite direction to the normal, ensuring that the damping effect is reasonable.

[0025] Preferably, the total force F tol The calculation formula is formula (6).

[0026] F tol =F rep +F ret+ F vis (6).

[0027] More preferably, when fluid particle i does not penetrate the wall, formula (6) can be simplified to formula (7).

[0028] F tol =F rep+ F vis (7).

[0029] More preferably, when the distance between the fluid particle i and the shell model wall reaches a critical value, the boundary repulsion force F rep=An, where A is the repulsion coefficient, controlling the magnitude of the repulsion; n is the boundary normal direction, pointing towards the fluid region. Formula (7) simplifies to formula (8).

[0030] F tol =An + F vis (8),

[0031] More preferably, when fluid particle i penetrates the wall, the boundary repulsion force F rep =An, where A is the repulsion coefficient, controlling the magnitude of the repulsion; n is the boundary normal direction, pointing towards the fluid region. Formula (6) simplifies to formula (9).

[0032] F tol =An+F ret+ F vis (9).

[0033] The beneficial effects of this invention are as follows:

[0034] 1. This invention boasts strong physical realism and can accurately simulate complex fluid-structure interaction processes. It decomposes the complex nonlinear penetration process of underwater contact explosions into three stages and matches the most suitable physical model to each stage:

[0035] (1) In the non-penetration stage (d0>d>0), the spatial repulsion model is used to apply conventional repulsion force to maintain its outward push, which avoids non-physical "adhesion" or premature penetration of fluid particles before contact, and ensures the accuracy of pressure field establishment.

[0036] (2) At the critical distance stage (d=0), the short-range force between the fluid particles and the fixed surface increases sharply, providing a high-precision physical criterion for possible subsequent penetration and enhancing the stability of the simulation.

[0037] (3) After penetration occurs (d < 0), a repulsive-restoring force coupling model is adopted in this process. The restoring force component is the core manifestation of viscoelastic behavior, simulating the elastic recovery energy of the shell structure material itself. Along the normal of the shell, it "pulls back" or "pulls back" the penetrated particles into the fluid domain. In this stage, through the coupling effect of the repulsive force component and the restoring force component, not only is the non-physical complete penetration and escape of particles prevented, but the "wetting surface change" and "structural rebound" phenomena that exist when fluids interact with flexible structures in the real world are also more accurately reproduced.

[0038] 2. This invention effectively suppresses non-physical penetration, ensuring computational stability and accuracy. This application constructs a dynamic, adaptive boundary protection layer through pre-emptive prevention of repulsive forces in the first two stages and post-emptive correction of restoring forces in the third stage. Even if individual particles break through the repulsive barrier due to extremely high local pressure (such as at the explosion center), the restoring force model can act as a last line of defense to correct them, rather than allowing them to escape. Simultaneously, it greatly enhances numerical robustness under extreme loads.

[0039] 3. This invention adds a viscous damping force model based on the velocity difference between fluid particles and boundary shell particles, introducing an energy dissipation mechanism and improving physical realism. The added viscous term is a damping force, which is proportional to the velocity of the fluid particle relative to the wall and in the opposite direction to the motion. When a particle attempts to bounce back after a collision, this damping force absorbs a portion of the particle's kinetic energy and dissipates its internal energy. This significantly reduces the particle's rebound velocity, simulating the kinetic energy dissipation caused by viscosity in real fluids, making the particle behavior more "stable" and eliminating non-physical continuous oscillations, effectively improving the numerical stability of boundary conditions.

[0040] 4. This invention constructs a "visco-elastic" composite model, in which the "repulsion-restoring force" model and the "viscous damping force" model complement each other perfectly, so that the boundary response has both mechanical support and energy dissipation, fundamentally enhancing the stability and convergence of the calculation. Attached Figure Description

[0041] Figure 1 This is a schematic diagram illustrating the repulsive and viscous forces experienced by fluid particles when they fail to penetrate the wall surface, according to the present invention.

[0042] Figure 2 This is a schematic diagram illustrating the repulsive and viscous forces experienced by fluid particles after penetrating a wall surface, according to the present invention.

[0043] Figure 3 This is a diagram illustrating the trajectory of fluid particles penetrating a wall, as simulated in this invention. Detailed Implementation

[0044] The specific embodiments of the present invention will now be described with reference to the accompanying drawings.

[0045] Example 1:

[0046] "Repulsion-Restoration Force Coupled Model": A method for handling the boundary conditions of SPH shell particles in underwater contact explosions, including: dividing the particle penetration process into three stages: when the fluid particle has not penetrated the wall, when the distance between the fluid particle and the shell model wall reaches a critical value, and when the fluid particle penetrates the wall.

[0047] Phase 1: When fluid particle i has not penetrated the wall, the spatial repulsion model proposed by Monaghan et al. is adopted, and the boundary repulsion force F based on displacement is... rep The nonlinear power function model is expressed as formula (1).

[0048]

[0049] Where A is the repulsion coefficient, controlling the magnitude of the repulsion force; d is the distance from the current particle to the boundary; d0 is the effective range of the repulsion force, which is taken as the core radius h. When a particle enters this range, the repulsion force begins to take effect; n is the exponential coefficient, with a value ranging from 1 to 4, and in this embodiment, it is taken as 2; n is the boundary normal direction, pointing towards the fluid region. At this time, the total force F tol =F rep .

[0050] When the fluid particles are relatively far from the wall, the repulsive force is weak or zero. As the particles enter the area of ​​influence, i.e., when the distance 0 < d < d0, a repulsive force begins to occur between the particles and the wall. At this point, the repulsive force increases rapidly as the distance between the particles and the wall decreases, preventing the fluid particles from approaching further. This stage employs a classical repulsive force model, where a repulsive force perpendicular to the boundary is applied between the particle center and the boundary when the fluid particles approach the boundary surface. The magnitude of the repulsive force is related to the distance of the particles from the boundary.

[0051] Second stage: When the distance between fluid particle i and the shell model wall reaches the critical value, d = 0 in formula (1), then formula (1) simplifies to formula (2).

[0052] F rep =An,d=0 (2)

[0053] Where A is the repulsion coefficient, controlling the magnitude of the repulsion force; n is the boundary normal direction, pointing towards the fluid region; at this time, the total force F tol =F rep .

[0054] When fluid particles "touch" the wall, the repulsive force reaches its peak or saturation value. At this stage, the boundary can be kept intact by the repulsive force alone. However, since the shell model is a single-layer particle boundary, it will lead to a lack of approximate accuracy in the calculation of the particle field. Furthermore, due to the inertia of the fluid particles, the phenomenon of particle penetration will still occur, that is, the negative distance range after the particle enters the wall will appear.

[0055] Third stage: When fluid particle i penetrates the wall: Construct a "repulsive force-restoring force coupling model", then the restoring force F ret The calculation expression is formula (3).

[0056] F ret =-kdV i(3), where k is the recovery coefficient, in N / m 4 ;d is the vector distance from the point of penetration into the boundary, pointing outwards from the boundary surface; V i Let F be the volume of the fluid particle. At this point, the total force F... tol The calculation formula is formula (4).

[0057] F tol =F rep +F ret (4)

[0058] During this process, the boundary repulsion force F rep If the value is fixed and its value is An, then substituting it into formula (4) can calculate the total force.

[0059] If the particle still penetrates the wall in the numerical simulation, a restoring force needs to be added in addition to the pure repulsive force to "pull back" the particle. Specifically, a linear restoring force proportional to the penetration depth is applied within the negative distance range after penetration, quickly pushing the particle back into the fluid region.

[0060] By employing a segmented coupling model of repulsive and restoring forces in three stages, fluid particles are prevented from actually entering the solid region, thus ensuring the accuracy of neighborhood search and field variable calculations. If a particle penetrates the wall, its neighborhood search will lose some fluid particles, leading to a sharp increase in estimation errors for local pressure, density, etc. However, after applying the restoring force, the penetrating particles are promptly pushed back into the fluid domain, remaining within the correct fluid region and restoring the neighborhood distribution to normal. Furthermore, this restoring force mechanism is similar to elastic collision, which can prevent particle aggregation at the boundary while ensuring no penetration, thereby reducing the kernel function approximation error caused by particle inhomogeneity at the boundary.

[0061] Example 2:

[0062] In this embodiment, to improve the stability and physical accuracy of fluid particles near the shell structure interface in further fluid-structure interaction, a viscous damping force model based on velocity difference is introduced on the basis of the original boundary repulsion force, forming a "visco-elastic" composite model of "repulsion force, restoring force, and viscous damping force". This model constructs a velocity-dependent damping dissipation force, for example, following Monaghan's idea of ​​artificial viscosity, adding a viscous term with reverse velocity during particle collision or collision tendency, to suppress the high-frequency oscillating behavior of particles penetrating at the boundary, effectively improving the numerical stability under boundary conditions.

[0063] Specifically, a viscous damping force model is constructed based on the velocity difference between fluid particle i and boundary shell model particle j. Then the viscous damping force F... vis The calculation formula is formula (5).

[0064]

[0065] Among them, v ij V is the relative velocity between fluid particle i and boundary shell model particle j; j Let r be the volume of the particle in the boundary shell model. ij It represents the relative position of fluid particle i and boundary shell model particle j; μ art ε is the viscous damping coefficient, controlling the dissipation intensity; N is the total number of neighboring particles of particle i, and ε is a finite quantity to prevent the denominator in formula (5) from being 0; v ij ·r ij This represents the relative motion component of the particle in the normal direction, and the direction of the force is always in the opposite direction to the normal, ensuring that the damping effect is reasonable.

[0066] Then the total force F tol The calculation formula is formula (6).

[0067] F tol =F rep +F ret+ F vis (6),

[0068] When fluid particle i does not penetrate the wall, equation (6) can be simplified to equation (7).

[0069] F tol =F rep+ F vis (7);

[0070] When the distance between fluid particle i and the shell model wall reaches a critical value, the boundary repulsion force F rep =An, Formula (7) simplifies to Formula (8),

[0071] F tol =An + F vis (8);

[0072] When fluid particle i penetrates the wall, the boundary repulsive force F rep =An,

[0073] Total force F tol =An+F ret+ F vis (9).

[0074] In this embodiment, a flat plate shell model is set up, and fluid particles from the fluid impact the plate at a velocity of v = -5.0 m / s. The support domain of the particles is set to 0.1 m (h = d0 = 0.1 m), the mass of the particles is 0.001 kg, and the volume of the particles is 0.001 m³. 3 The time step is 1.0e-4 s. The repulsion coefficient A is set to 0.2, and the viscous damping coefficient μ art The value is set to 0.2, the maximum repulsive force range is set to the size of its support domain, and the initial distance of the particle from the plate shell is 0.2m.

[0075] The dynamic behavior of fluid particles near the contact boundary is then simulated using this viscoelastic composite model, yielding the following results: Figure 1 The results are shown in the figure. It can be seen from the figure that when the fluid particles have not yet contacted or are just approaching the boundary of the shell model, they are subjected to a boundary repulsive force F. rep With viscous damping force F vis The combined effect of these factors effectively suppressed its excessive approach to the boundary or high-frequency oscillation behavior. However, when fluid particles penetrate and enter the shell model, the original boundary repulsive force F... rep If it no longer increases and remains a constant, then the restoring force F ret and viscous damping force F vis The combined effect of these factors pulls the fluid particles back to their original fluid region, preventing them from remaining in the invalid computational domain for an extended period.

[0076] The trajectory of a fluid particle from a distance to its penetration of the shell within one second is recorded. The trajectory diagram showing the changes in its position, velocity, and the boundary forces acting on it over time is shown below. Figure 3 As shown, the particle's velocity gradually decreases as it approaches the boundary, and it penetrates the shell element in 0.04 s before being rapidly pulled back. This avoids the problem of particle escape or unclear interpenetration with the boundary, and the particle eventually stabilizes at a certain distance from the shell surface, reaching a new equilibrium state. This process fully demonstrates that the proposed shell-particle viscoelastic composite dynamic boundary condition based on the repulsive-restoring force coupling mechanism and velocity-related viscous damping can effectively simulate the physical interaction between particles and the boundary, preventing particle penetration and enhancing the stability and physical rationality of the simulation.

[0077] It should be noted that d=0 is a theoretical critical point. Numerically, d is very close to zero or just turns negative when the phase transition is triggered.

[0078] The above description is an explanation of the present invention and not a limitation thereof. The scope of the present invention is defined by the claims. Within the scope of protection of the present invention, any form of modification may be made.

Claims

1. A method for handling SPH shell particle boundary conditions for underwater contact explosions, characterized in that: The following operational procedures are included: The particle penetration process is divided into three stages: when the fluid particle has not penetrated the wall, when the distance between the fluid particle and the shell model wall reaches a critical value, and when the fluid particle penetrates the wall. When fluid particle i does not penetrate the wall: using the spatial repulsion model, the boundary repulsion force F based on displacement is... rep The nonlinear power function model is expressed as formula (1). Where A is the repulsive force coefficient, controlling the magnitude of the repulsive force; d is the distance from the current particle to the boundary; d0 is the range of the repulsive force; n is the exponential coefficient; and n is the boundary normal direction, pointing towards the fluid region. At this moment, the total force F tol =F rep ; When the distance between fluid particle i and the shell model wall reaches a critical value: d = 0 in formula (1), then formula (1) simplifies to formula (2). F rep =An,d=0 (2), Where A is the repulsion coefficient, which controls the magnitude of the repulsion force; n is the boundary normal direction, pointing towards the fluid region; At this moment, the total force F tol =F rep ; When fluid particle i penetrates the wall: Constructing a "repulsive force-restoring force coupling model", the restoring force F ret The calculation expression is formula (3). F ret =-kdV i (3), Where k is the recovery coefficient, in N / m 4 d represents the vector distance from which the particle penetrates into the boundary. From the point of penetration outwards from the boundary surface; V i Let be the volume of the fluid particle. At this moment, the total force F tol The calculation formula is formula (4). F tol =F rep +F ret (4)。 2. The method for handling SPH shell particle boundary conditions for underwater contact explosions as described in claim 1. Its features are: When fluid particle i penetrates the wall, the boundary repulsive force F rep It is a fixed value, and its value is A. n， Where A is the repulsion coefficient, which controls the magnitude of the repulsion force; n is the boundary normal direction, pointing towards the fluid region.

3. The method for handling SPH shell particle boundary conditions for underwater contact explosions as described in claim 1. Its features are: In formula (1), d0 is taken as the nuclear radius h. When a particle enters this range, the repulsive force begins to take effect.

4. The method for handling SPH shell particle boundary conditions for underwater contact explosions as described in claim 1. Its features are: The exponential coefficient n in formula (1) ranges from 1 to 4.

5. The method for handling SPH shell particle boundary conditions for underwater contact explosions as described in claim 4. Its features are: The exponential coefficient n in formula (1) takes the value of 2.

6. The method for handling SPH shell particle boundary conditions for underwater contact explosions as described in claim 1. Its features are: Construct a viscous damping force model based on the velocity difference between fluid particle i and boundary shell model particle j, then the viscous damping force F vis The calculation formula is formula (5). Among them, v ij V is the relative velocity between fluid particle i and boundary shell model particle j; j Let r be the volume of the particle in the boundary shell model. ij It represents the relative position of fluid particle i and boundary shell model particle j; μ art ε is the viscous damping coefficient, controlling the dissipation intensity; N is the total number of neighboring particles of particle i, and ε is a finite quantity to prevent the denominator in formula (5) from being 0; v ij ·r ij This represents the relative motion component of the particle in the normal direction, and the direction of the force is always in the opposite direction to the normal, ensuring that the damping effect is reasonable.

7. The method for handling SPH shell particle boundary conditions for underwater contact explosions as described in claim 6, characterized in that: Total force F tol The calculation formula is formula (6). F tol =F rep +F ret+ F vis (6)。 8. The method for handling SPH shell particle boundary conditions for underwater contact explosions as described in claim 7, characterized in that: When fluid particle i does not penetrate the wall, equation (6) can be simplified to equation (7). F tol =F rep+ F vis (7)。 9. The method for handling SPH shell particle boundary conditions for underwater contact explosions as described in claim 7, characterized in that: When the distance between fluid particle i and the shell model wall reaches a critical value, the boundary repulsive force F rep =An, where A is the repulsion coefficient, controlling the magnitude of the repulsion; n is the boundary normal direction, pointing towards the fluid region. Formula (7) simplifies to formula (8). F tol =The + F vis (8)。 10. The method for handling SPH shell particle boundary conditions for underwater contact explosions as described in claim 1, characterized in that: When fluid particle i penetrates the wall, the boundary repulsive force F rep =An, where A is the repulsion coefficient, controlling the magnitude of the repulsion; n is the boundary normal direction, pointing towards the fluid region. Formula (6) simplifies to formula (9). F tol =The+F ret+ F vis (9)。

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