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CN-121997841-A - High-order interface capturing method for coupling level set and fluid volume based on mixing precision

CN121997841ACN 121997841 ACN121997841 ACN 121997841ACN-121997841-A

Abstract

The invention relates to a high-order interface capturing method based on mixed precision and coupling a level collector and a fluid volume, which comprises the steps of firstly dividing a calculation area into grids comprising a plurality of control body units, initializing, then identifying an interface unit, adopting a high-order polynomial to reconstruct a THINC interface function based on an LS value, then introducing a mixed precision iterative algorithm to solve an interface position nonlinear equation, ensuring self-adaptive switching to multi-precision operation to obtain a robust solution when double precision cannot be converged, then calculating flux by utilizing an accurate interface and solving a VOF transport equation, ensuring mass conservation, and finally directly reconstructing an LS field without reinitialization by a pure geometric method such as generating an interface point cloud, searching a nearest point and the like through projection in a narrow band based on predicted interface geometry. The invention obviously improves the capturing precision and geometric fidelity of complex interfaces such as high curvature, sharp corners and the like on the unstructured grid, and has high precision and strong robustness.

Inventors

  • CHEN DEZHU
  • XIE BIN
  • LIAO SHIJUN

Assignees

  • 上海交通大学

Dates

Publication Date
20260508
Application Date
20260317

Claims (10)

  1. 1. The high-order interface capturing method for coupling the level set and the fluid volume based on the mixing precision is characterized by comprising the following steps of: s1, dividing a calculation area into grids comprising a plurality of control body units; S2, initializing a VOF field, an LS field and a speed field of each control body unit; S3, identifying an interface unit, and reconstructing a THINC interface function on the interface unit by adopting a high-order polynomial based on LS values of the centers of all control body units on a preset template; s4, establishing a nonlinear equation about an interface position in the interface unit according to the constraint relation that the THINC interface function and the VOF field meet volume fraction conservation; S5, solving the nonlinear equation by adopting a mixed precision iterative algorithm to obtain a converged interface position, wherein the mixed precision iterative algorithm is adaptively switched to multi-precision operation when double-precision operation cannot be converged; s6, determining a THINC interface function at the current moment based on the interface position obtained in the S5, calculating interface flux based on the THINC interface function at the current moment, and obtaining a VOF field at the next moment by solving a VOF transport equation; s7, predicting the interface geometry of the next moment based on the THINC interface function and the speed field at the current moment; S8, directly reconstructing an LS field of the next moment through a geometric method in a preset narrow-band area surrounding the interface based on the predicted interface geometry of the next moment, wherein the geometric method comprises the steps of generating a point cloud near the interface, and searching a nearest point of the center point on a continuous interface represented by the high-order polynomial for the center point of the control body unit; s9, repeating the steps S3-S8 to achieve evolution capture of the interface.
  2. 2. The method for capturing a high-order interface based on coupling a level collector and a fluid volume with mixed precision according to claim 1, wherein the control body unit is a polygonal or polyhedral unit of arbitrary shape.
  3. 3. The method for capturing a high-order interface based on coupling a level set and a fluid volume with mixed precision according to claim 1, wherein in S3, the higher order polynomial is a quadratic or cubic polynomial.
  4. 4. The method for capturing a high-order interface based on coupling a level set and a fluid volume with mixed precision according to claim 3, wherein when the interface is reconstructed by using a cubic polynomial, the implementation manner comprises: Firstly solving to obtain low-order term coefficients; calculating a cubic term coefficient based on the low-order term coefficient; and finally, correcting the low-order term coefficient to realize the polynomial reconstruction with higher overall accuracy.
  5. 5. The hybrid precision based high order interface capture method of coupling a level set and a fluid volume of claim 1, wherein in S5 the hybrid precision iterative algorithm comprises: solving the nonlinear equation by adopting a second-order homolunar iterative formula under double precision; if the nonlinear equation fails to converge under the double precision, performing variable translation transformation on the nonlinear equation, and then iteratively solving the nonlinear equation under the double precision again; And if the variable translation is not converged, self-adaptive switching to multi-precision operation, wherein the effective bit number of the multi-precision operation is dynamically determined according to the absolute value of the polynomial value at the integration point in the nonlinear equation.
  6. 6. The method for capturing the high-order interface based on the coupling level set and the fluid volume with the mixed precision according to claim 5, wherein in the multi-precision operation, an iterative formula of a dynamic convergence control parameter is adopted for solving, and the dynamic convergence control parameter is automatically updated by solving an auxiliary equation in each iteration.
  7. 7. The method for capturing the high-order interface based on the coupling level of the mixed precision and the fluid volume according to claim 1, wherein in S8, the LS field at the next moment is directly reconstructed by a geometric method, specifically comprising: S81, calculating to obtain an LS value at a vertex based on the LS field, acquiring an intersection point of an interface and a unit edge according to the LS value at the vertex, and then sampling on an intersection point connecting line to generate an initial point cloud; s82, projecting the initial point cloud to a continuous interface represented by the high-order polynomial to obtain an interface point cloud positioned on the continuous interface; s83, searching a discrete closest point from the interface point cloud for the center point of the control body unit; S84, taking the discrete closest point as an initial value, carrying out iterative search on the continuous interface to obtain a true closest point of the center point, and calculating the distance of the true closest point as an LS value at the center point.
  8. 8. The hybrid precision based high order interface capture method of coupling level collectors and fluid volumes of claim 7, wherein in S84, searching for the true closest point on the continuous interface is accomplished by creating and solving a constrained optimization problem comprised of lagrangian multipliers.
  9. 9. The hybrid precision based high order interface capture method of coupling a level collector and a fluid volume of claim 1, wherein in S8 the preset narrowband region comprises an interface unit, a first layer of neighbor units sharing vertices with the interface unit, and a second layer of neighbor units sharing vertices with the first layer of neighbor units.
  10. 10. A readable storage medium, on which a computer program is stored, characterized in that the computer program, when executed, is capable of implementing a high-order interface capturing method based on a coupling level set and a fluid volume of a hybrid precision according to any one of claims 1-9.

Description

High-order interface capturing method for coupling level set and fluid volume based on mixing precision Technical Field The invention relates to the technical field of computational fluid mechanics, in particular to a high-order interface capturing method for coupling a level set and a fluid volume based on mixing precision. Background In computational fluid dynamics, accurate simulation of multiphase flows (e.g., gas-liquid flows, droplet collisions, spray processes, etc.) involving dynamic interfaces is a central challenge for numerous engineering and scientific applications. The interface capturing technology is used for implicitly representing an interface under the Euler framework and becomes a key tool for solving the problems, and the aim is to accurately track the position, geometric characteristics and evolution of the interface in a complex flow field. Currently, existing interface capturing methods mainly include a Volume of Fluid (VOF) method, a Level Set (LS) method, and a coupled VOF and LS method (i.e., CLSVOF method). The VOF method represents a two-phase distribution by a volume fraction field, and has the greatest advantage of strictly guaranteeing mass conservation. The VOF method based on geometric reconstruction is characterized in that interfaces are explicitly reconstructed through techniques such as piecewise linear interface calculation, so that numerical dissipation is reduced, and the method is the most widely applied method. However, conventional geometric VOF methods are generally based on linear or planar interface assumptions, which can produce significant geometric errors in processing interfaces with high curvature or sharp features. Although surface reconstruction algorithms have been proposed to improve accuracy, these methods are generally computationally complex and are mainly limited to structured grids, which are difficult to popularize to unstructured grids. The LS method characterizes the interface by introducing a smooth symbolic distance function, and the function has good mathematical properties, so that geometric quantities such as normal vectors and curvatures of the interface can be calculated with high precision. However, the LS method suffers from the property that the sign distance function is destroyed after the transport equation is solved numerically, and must be restored by an additional "re-initialization" process. This step introduces numerical errors, resulting in interface offset and mass non-conservation, and is computationally time consuming, with strong parameter dependence. In order to achieve both mass conservation and geometric accuracy, a method of coupling Level Set and VOF has been developed, which is called the Coupled LEVEL SET AND Volume of Fluid (CLSVOF) method. The existing CLSVOF methods can be divided into two types, namely algebraic-based VOF and geometric-based VOF, according to the difference of the VOF parts. The CLSVOF method based on algebra is easy to realize on unstructured grids, but LS fields are constructed through algebraic formulas, and the geometric accuracy is insufficient and the parameters are sensitive. Although the CLSVOF method based on the geometric VOF can carry out explicit interface reconstruction, the reconstruction interface is mostly linear, the high-order curved surface expression is difficult to realize, and the dilemma that the geometric operation is complex and difficult to realize on the unstructured grid is also faced. In recent years, research is attempted to introduce curve or curved surface interface reconstruction to improve the precision, but the application range of the method is still limited to structured grids, and the fundamental difficulty of realizing high-order curved surface expression on general unstructured grids is not solved. In addition, the strategy based on the coupling of the THINC function and the LS provides a new idea for constructing the high-order interface representation. The THINC method utilizes a function with analytical expressions to construct an interface, and natural support extends to higher order polynomials. However, the existing THINC-LS method still does not depart from the evolution framework of the traditional LS method, and still relies on complex partial differential equation numerical solution and reinitialization processes to maintain LS field properties, so that the algorithm is complex and difficult to expand to an unstructured grid. Meanwhile, how to efficiently and robustly construct a geometric LS field based on a high-order THINC interface and how to ensure the convergence of the interface position equation solving under extreme parameters is still a technical bottleneck to be solved. In summary, in the process of pursuing high precision and high fidelity, the existing interface capturing technology generally faces the following challenges: 1) It is difficult to implement a higher order surface interface representation on an unstructured grid; 2) The