CN-121981026-A - Hydrodynamic numerical simulation method based on high-order exponential type combined compact differential format

CN121981026ACN 121981026 ACN121981026 ACN 121981026ACN-121981026-A

Abstract

The invention discloses a hydrodynamic numerical simulation method based on a high-order exponential type combined compact differential format, and belongs to the technical field of hydrodynamic simulation. The method comprises the steps of establishing a control equation and a discrete model in a speed-vortex form based on a three-dimensional unsteady incompressible Navier-Stokes equation, dividing a calculation domain by adopting a 19-point grid node template, utilizing a dimension reduction method to combine with Taylor series expansion to derive a spatial six-order exponential type combined compact differential format, fusing an alternating direction implicit ADI, approximate factorization and regional decomposition parallel strategy to construct a discrete format with time second-order to third-order precision, solving a partial derivative by a preprocessed stable bi-conjugate gradient iterative algorithm, and adopting a self-adaptive error threshold and residual error convergence rate combined convergence criterion to achieve efficient coupling solving of a speed field and a vortex field. The invention reduces the calculation complexity and the memory consumption while maintaining the high-order precision.

Inventors

PENG YAXIN
DING ZHIHONG
PENG YAN
WEI HONGYU
SHENG BIN
MA ZHIYING
ZHENG JIANYONG

Assignees

上海大学

Dates

Publication Date: 20260505
Application Date: 20260409

Claims (10)

1. A hydrodynamic numerical simulation method based on a higher-order exponential-type combined compact differential format, comprising: step 1, establishing a control equation and a discrete model in a speed-vortex form based on a three-dimensional unsteady incompressible Navier-Stokes equation; step 2, setting corresponding technical parameter boundary conditions and initial conditions for the discrete equation set according to physical characteristics of the cylindrical bypass flow; step 3, dividing a calculation domain by adopting a 19-point grid node template, wherein the space direction adopts an equidistant step length or a non-uniform step length, and the time division adopts an equidistant step length; step 4, separating space variables according to the sequence of flow direction, normal direction and direction expansion by using a dimension reduction method, reserving cross terms, rewriting a steady form of a convection diffusion equation into an equivalent equation set, expanding to a six-order truncation error through Taylor series, and carrying out merging operation to obtain a space six-order exponential type combined compact differential format in a deduction mode; step 5, constructing a time discrete format by adopting Taylor series expansion and remainder correction technology and combining an alternate direction implicit ADI and approximate factorization method; step 6, initializing parameters, carrying out Gaussian filtering pretreatment on an initial speed field, and calculating the initial speed field and the vorticity field by using initial conditions and boundary conditions; Step 7, respectively calculating first-order partial derivatives and second-order partial derivatives of the inner points and the boundary points through a stable bi-conjugate gradient BICGSTAB iterative algorithm; step 8, calculating a boundary point function value, substituting the boundary point function value into an ADI format to calculate an intermediate value, updating a partial derivative, and then verifying whether the norm of the absolute error of the function value meets a convergence criterion; And (7) repeating the steps 7-8 until all time steps are calculated, and outputting a numerical solution of the speed field and the vorticity field.
2. The method for simulating fluid dynamics based on high-order exponential-type combined compact differential format according to claim 1, wherein the computational space is obtained by coordinate transformation The following three-dimensional unsteady Navier-Stokes equation velocity-vortex form: ; Wherein the convection flux Viscous flux Space, space The flow direction, the normal direction and the spanwise direction are respectively.
3. The method for simulating the hydrodynamic values based on the higher-order exponential-type combined compact differential format according to claim 1, wherein the step 3) adopts a 19-point grid node template to divide the calculation domain specifically comprises: The calculation domain is divided by adopting a 19-point grid node template, wherein the template takes a target node as a center, and adjacent nodes are symmetrically expanded in three spatial directions, so that adjacent point information coverage required by spatial sixth-order precision is ensured.
4. The method for simulating fluid dynamics based on the higher-order exponential-type combined compact differential format according to claim 1, wherein, The derivation process of the spatial sixth-order exponential-type combined compact differential format in the step 4 is that the space variable is separated from the steady form of the convection diffusion equation, the cross terms are reserved, the space discrete format is obtained by expanding to the sixth-order truncation error through Taylor series, and the space discrete format is obtained by combining.
5. The method of claim 1, wherein the step of performing the Taylor-series expansion to a sixth-order truncation error and merging operation comprises: A Taylor series expansion and remainder correction technology is adopted to construct a time discrete format, wherein in the initial stage, when the time layer n=1, a second-order precision ADI format is adopted due to insufficient time step accumulation, and when n is more than 2, the time discrete format is switched to a third-order precision ADI format.
6. The method for simulating fluid dynamics based on the higher-order exponential-type combined compact differential format according to claim 1, wherein, The iterative solution of the discrete unsteady equation by adopting the time advance method ADI comprises the steps of solving a predicted value of the vortex flow field of the next time step by utilizing the speed and the vortex flow field of the current time step and using a vortex flow transport equation of a high-order exponential combination compact differential format discrete in each time step, substituting the newly obtained predicted value of the vortex flow field as a source term into a poisson speed-vortex flow relation equation of the high-order exponential combination compact differential format discrete, solving a high-precision speed field of the next time step, and repeating the process until the flow field is developed to a statistically unsteady state.
7. The method for simulating fluid dynamics based on the higher-order exponential-type combined compact differential format according to claim 1, wherein, And step 8, the convergence criterion is a combined convergence criterion of the adaptive error threshold and the residual error convergence rate.
8. The method for simulating fluid dynamics based on the higher-order exponential-type combined compact differential format according to claim 1, wherein, When the calculation domain is divided by adopting the non-uniform step length, the non-uniform grid is adapted through format coefficient correction, and the spatial sixth-order precision is ensured.
9. The method for simulating fluid dynamics based on the higher-order exponential-type combined compact differential format according to claim 1, wherein, Aiming at a variable fluid flow scene, the accurate simulation of variable diffusion coefficient flow is realized through viscosity flux term correction.
10. A computer-readable storage medium, characterized in that the storage medium stores a computer program which, when executed by a processor, implements the method of any one of claims 1-9.

Description

Hydrodynamic numerical simulation method based on high-order exponential type combined compact differential format Technical Field The invention relates to the technical field of hydrodynamic simulation, in particular to a hydrodynamic numerical simulation method based on a high-order exponential type combined compact differential format. Background In recent years, in the field of hydrodynamic simulation, numerical simulation of incompressible Navier-Stokes equations, finite difference method, finite volume method and finite element method constitute the main stream technical framework. The Direct Numerical Simulation (DNS) has unique value in revealing complex flow physical mechanism because of the capability of resolving a full-scale flow structure without a turbulence model, namely, the DNS can provide high-precision flow field details whether airfoil streaming in aerospace, combustion oscillation in power engineering and pollutant diffusion in environmental fluid. However, achieving high precision resolution also places higher demands on the performance of the digital method. In engineering Computational Fluid Dynamics (CFD) practice, a Compact Differential Method (CDM) can achieve higher precision than a traditional format under the same grid scale by utilizing more adjacent point information, and meanwhile, numerical dissipation and dispersion errors are effectively restrained, so that obvious advantages are shown on capturing fine flow structures such as vortex street evolution, shock boundary layer interference and the like. With the gradual integration of the method in industrial software, the boundary processing technology and the format construction theory are also mature. For solving the high-dimensional unsteady problem, the combination of the high-order CDM and the Alternating Direction Implicit (ADI) method becomes an important technical path. According to the strategy, the multi-dimensional problem is directionally decoupled, the complex global solution is converted into a series of one-dimensional calculation, and the calculation load is greatly reduced while the numerical stability is improved. The technology is successfully applied to engineering scenes such as impeller mechanical inflow and combustion instability analysis, and the adaptability to variable-property flow is further enhanced by combining a pretreatment technology. The exponential type compact differential format (ECFDS) is taken as an important development of CDM, and is naturally embedded into windward effect by introducing an exponential weight function, so that the exponential type compact differential format is outstanding in large gradient flow simulation of boundary layers, shear layers and the like. From the initial successful application in the convection-diffusion equation to the subsequently developed fourth order perturbation index format, the series of methods progressively enhances the numerical robustness to strong convection conditions. Aiming at the common variable diffusion coefficient problem in actual engineering, the related improved format is also adjusted through the self-adaptive index term, so that the calculation precision and stability are maintained. In order to further expand the application boundary of the high-dimensional problem, the new generation high-order exponential compaction format fully utilizes the local attenuation characteristic of the exponential function, and remarkably inhibits the pseudo-numerical diffusion introduced by discrete convection terms, so that the simulation of convection dominant flow on a relatively sparse grid is possible. By combining with the ADI method, the developed three-dimensional unsteady problem solver effectively controls memory occupation and calculation cost while maintaining high-precision characteristics. The technical route is further extended to three-dimensional quasi-linear parabolic equations, and the processing capacity of nonlinear evolution problems is enhanced through an implicit time-push strategy. In the aspect of practical engineering application, the exponential compacting format is successfully used for solving the numerical values of a two-dimensional Burgers equation and a Navier-Stokes equation, an exponential discrete mechanism of the exponential compacting format effectively stabilizes non-physical oscillation caused by nonlinear convection, and the vortex generation evolution process is accurately reproduced in classical examples such as cylindrical streaming, backward step streaming and the like. Aiming at the grid adaptability problem caused by complex geometric shapes, the precision loss phenomenon near the curve boundary is remarkably relieved by the coefficient reconstruction technology through the exponential compaction format on the non-uniform grid. However, although ECFDS series of methods show colors in theoretical research and standard computing examples, the comprehensive integration of the method in engineering CFD s