34 results about "Systems of partial differential equations" patented technology

The invention relates to a flight icing numerical value simulation method of a helicopter rotor wing. The flight icing numerical value simulation method is mainly characterized by comprising the following steps that: a vorticity compensation force algorithm is added into a momentum equation and an energy equation in a single fluid model used for vortex movement used for simulating air-super cold water drop two-phase flows under a rotating coordinate system in rotor wing trail traces, and a centrifugal force and geostrophic force algorithm is added into a super cold water drop sliding velocity equation; a water film movement and icing model of the centrifugal force and the geostrophic force is considered; and the algorithms and the models are used for carrying out the flight icing numerical value simulation flow process of the helicopter rotor wing, wherein the model of single fluid two-phase flowing used for simulating the simulating air-super cold water drop movement is realized by a partial differential equation group for describing the movement of air and air-super cold water drop binary mixtures in a rotor wing tail trace flow field, and a two-phase flow slipping speed model. The condition that the quality and energy changes are generated in water films and ice layers because of the rotary movement of the rotor wing is considered in the model of the water film movement and icing process on the rotor wing surface, and the icing shape of the rotor wing surface is obtained.

The invention discloses a distribution type multi-sensing cooperation testing method and a system thereof; the method includes the following steps that: a multi-sensing cooperation testing model is established; area vectors of the area are obtained, and the area vectors of the area are automatically converted to the adjoint vectors; a plurality of systems of partial differential equations are converted to one or a plurality of sequence parameter equations, by the self organization evolution of sequence parameters, a macrostructure is created and a general calculation formula of the uncertain problem decision-making is obtained, wherein a 'cooperation-competition-coordination' process based multi-sensing cooperation testing mechanism model is established, which forms a three-layer reaction type cooperation testing method. The system includes that the data communication is made in the mode of the IPv4/IPv6 based Ethernet, wherein the whole network testing platform comprises a filed test control layer, an enterprise-level monitoring layer and a remote test control layer.

The invention relates to the field of acoustics, in particular to a method for quickly calculating characterization and transfer of uncertainties of marine environment and sound fields. The invention aims to solve the problems of random spectrum characterization of uncertain environmental parameters and uncertain sound pressure fields and whether to transfer the uncertainties form the environmental parameters to the sound pressure fields. The method comprises the following steps of: establishing a domain space taking the known quantity as a center for the uncertain environmental parameters and the uncertain sound pressure fields respectively; performing the probability density function description on the uncertain quantity; and chaotically carrying out the random spectrum characterization according to a polynomial taking the probability density function as the uncertain quantity, and further combining the chaotic random spectrum characterization of the polynomial and a certain wave equation, educing the random wave equation embedded with uncertainty, acquiring the system of partial differential equation of uncertain coefficients, and finally acquiring the uncertain sound pressure fields formed by the linear superposition of the chaos based function of the uncertain coefficient weighting polynomial. The method has the advantages that: the acquired uncertain sound pressure fields are the same as the result acquired by MonteCarlo, and the calculating speed of the method is improved by more than 10 times.

The invention relates to an engine simulation design method. The method comprises the following steps that for any selected engine components, an engine power diagram and paths of air flowing through an engine are drawn, and the output end of one component is connected to the input end of the next component through a connecting joint; the function relationship between program input, system variables and specified characteristics of the components is obtained according to the mutual connection relation of all the components; calculation is carried out through the function relationship, so that a simultaneous algebra transcendental equation and partial differential equation set to be solved is obtained; the equations and/or the equation set are/is solved, and the parameters of all joints and an overall performance parameter of the whole engine are obtained. According to the engine simulation design method, the relative programs of heat exchange calculation of a by-pass heat exchange component is added, calculation precision is improved, technical parameters are provided for related manufactures producing engines in the process of troubleshooting of the same series, the method serves the actual production, the working efficiency of calculation of engine performance is improved greatly, and the deep developing capacity of the engine is improved.

The invention brings forward an online measurement method of residual stress of a conductive thin film material, and a corresponding measurement apparatus. A measurement structure is designed by use of an electrostatic driving Pull-in principle, relevance of parameters of two measurement members is controlled through use of synchronous processing control, through limiting correlation parameters of total strain energy of the two measurement members, a partial differential equation set of the total strain energy is constrained accordingly, and values of unknown residual stress sigma 0 and a Young's modulus E of the two measurement members are obtained through a mode of solving the partial differential equation set. According to the invention, the problem of incapability of real-time measurement of the conductive thin film material under the condition of unknown material parameters, unknown residual stress size and unknown positivity and negativity (tensile stress or compression stress) is solved. The apparatus and method have the advantages of simple measurement structure, simple electric signal loading and measurement, stable calculation method and high measurement efficiency.

The invention relates to a high accuracy surface modeling method based on big data. The method comprises the following steps: creating geographic coordinate information and to-be-tested variable sampling values of all sampling points; turning a to-be-tested regional space into a grid point form through discretization, and establishing a sampling equation; conducting high order difference discretization on a partial differential equation set of a surface, obtaining a corresponding algebraic system, combining the algebraic system and the sampling equation to form an equality constrain least squares problem, converting the problem into a solve cross cutting object function minimum value problem, and then converting the minimum value problem into a solve symmetry indeterminate equation set; randomly selecting iteration initial values; blocking a coefficient matrix, and storing the block matrixes after decomposition; solving an HASM equation set through a block line projection iterative method, and determining whether a solving result is convergent; determining whether a solution meets demands of a Gauss and C.odazzi equation set; and outputting a high accuracy simulation surface model. Large-scale problems can be solved, the needed storage space is small, and defects of HASM for solving large-scale problems are prevented.

The invention relates to a VLSI global layout model establishing method based on an explicit solution of a Poisson equation, comprising: representing the circuit as a hypergraph model; simulating theVLSI circuit layout model as a two-dimensional electrostatic system, and converting the density constraint into the constraint of the total potential energy N(v) equal to 0 of the electrostatic system; establishing partial differential equations based on the Poisson equation, boundary conditions and compatibility conditions; establishing an analytical formula of density functions and substitutinginto the partial differential equations; determining expressions of the potential and electric field according to the density functions; determining the convergence of the expressions of the potentialand electric field; solving the expressions of the potential and electric field according to the partial sum; obtaining the potential and electric field values of each grid by the fast calculation method, obtaining the potential and electric field of the module by weighting, and establishing the VLSI circuit layout model under the action of electric field force. The invention may provide an efficient and practical global layout result, and especially for large-scale examples, may meet the requirements of the current VLSI global layout stage.

The invention belongs to the technical field of numerical calculation of surface acoustic wave filters, and particularly relates to a frequency response characteristic analysis method of a surface acoustic wave resonator based on a dimensionality reduction PDE model. The method comprises the steps of: obtaining the structural data of a surface acoustic wave resonator; inputting the data into a dimension reduction PDF model to obtain a partial differential equation set representing the surface acoustic wave resonator; solving the partial differential equation set by adopting a finite element method to obtain a system matrix representing the surface acoustic wave resonator; adopting a finite element degree-of-freedom compression method and an order reduction technology to eliminate the degree-of-freedom needing no attention on the system matrix, and adopting periodic boundary conditions to eliminate the degree-of-freedom of left and right boundaries to obtain a system matrix equation after the degree-of-freedom is eliminated; solving the system matrix equation to obtain frequency response characteristics of the surface acoustic wave resonator. According to the method, irrelevant degree-of-freedom are eliminated by adopting the finite element degree-of-freedom compression method and the order reduction technology, and a uniform residual sound field can be realized in a directivity area.

The invention discloses a seabed hydrothermal fluid circulation three-dimensional simulation method, and relates to a simulation technology for simulating fluid behaviors and a circulation evolution process in a seabed hydrothermal system based on a physical mode. A kinetic control equation set of hydrothermal fluid in an ocean shell, namely a mass conservation equation, a momentum conservation equation and an energy equation, is solved, the thermodynamic property of the fluid is updated by utilizing a state equation (IAPWS-IF97) of water, and simulation calculation of hydrothermal circulationis completed. The solution of the partial differential equation set is based on an OpenFOAM platform, so that three-dimensional model simulation, cross-platform calculation and parallel calculation of multi-format complex grids are supported. Therefore, the invention provides an important simulation technical means for researching submarine hydrothermal circulation dynamics and associated mineralization rules thereof.

The invention relates to a method and equipment for realizing underground fluid flow numerical simulation based on a fractured porous medium fluid mathematical model and a storage medium. The method comprises the following steps: (1) constructing the fractured porous medium fluid mathematical model, according to the characteristics of the fractured porous medium, providing a set of partial differential equations describing fluid flow; (2) realizing underground fluid flow numerical simulation through the fractured porous medium fluid mathematical model constructed in the step (1). According to the model provided by the invention, the physical phenomena involved in the flowing process are comprehensively considered, and the physical phenomena are represented through the mathematical model, so that the description of the real physical process is more accurate, and the risk of poor numerical simulation effect caused by the inaccurate model is effectively relieved.

Based on the problem that the zinc reduction physicochemical reaction process of a zinc oxide volatilization kiln cannot be accurately characterized due to the characteristics of multiple variables, large time delay, nonlinearity and the like in the production process of the zinc oxide volatilization kiln, the invention provides a hybrid modeling method of mechanism modeling and key parameter fitting. According to the invention, based on research on a volatilization kiln structure, a production process, an internal physical and chemical reaction process and a heat and mass transfer mechanism,the hybrid modeling is that a partial differential equation set of mass conservation and energy conservation of the zinc oxide volatilization kiln and a hybrid model for fitting key parameters based on a support vector machine regression algorithm are established, wherein the key parameters are obtained by collecting kiln equipment parameters and production experiment data of a certain smelting enterprise; and with the hybrid modeling method, the defect that the model is difficult to accurately characterize by pure mechanism modeling is overcome, the defect that the operation mechanism and thereaction process in the kiln are difficult to characterize by pure data-driven modeling is also overcome, and the stability characteristic of the volatilization kiln and the dynamic characteristic ofthe production process can be accurately reflected.

The invention discloses a design method for a large-view non-distortion rearview mirror. The method includes the steps that initial design parameters are input and set; based on a light ray reflection basic principle, a system of partial differential equations is established; according to the initial design parameters, image points and coordinate algebraic expressions of object point coordinates, the system of partial differential equations is solved through a step-by-step integration method and according to an appointed integral path, and height values of all discrete points on a mirror face of the designed rearview mirror are obtained; after deviation of the height values of all the discrete points on an xy plane is eliminated, rotary and symmetric polynomial fitting is conducted; and an equation of the face shape of the smooth and continuous large-view rearview mirror is obtained, and data required for machining of a numerical control machine tool are generated. The requirements for image non-distortion, the large view and the distance reality sense can be met at the same time, the rearview mirror which has the reasonable view amplification multiplying power and accords with the habits of a driver can be designed, and the rearview mirror can be used as any of outer rearview mirrors and inner rearview mirrors on the left side and the right side of various types of vehicles and can adapt to various appearances and sizes.

The invention relates to a numerical simulation method for acidification of a double-mineral-component carbonate reservoir, which belongs to the field of numerical simulation of oil and gas field reservoir transformation, and comprises the following steps: (1) simplifying mineral distribution in reservoir rock, dividing the pore volume in a unit into equivalent pore volumes of corresponding minerals according to the initial mineral content, and solving the equivalent porosity of each mineral; (2) establishing a double-scale continuous medium model for acidification of the double-mineral-component carbonate reservoir; (3) establishing a geometric model, dividing the geometric model into triangular grids by using a Delaunay method, and setting initial and boundary conditions on the geometric model; and (4) obtaining reservoir and acid liquid parameters, inputting the parameters into the model, and jointly solving a partial differential equation set through a finite element method to obtain an acidification numerical simulation result. According to the method, the complexity of carbonate rock mineral composition is considered, unification of acidification numerical models of carbonate rocks with different mineral components is achieved, and the method has great significance in carbonate rock reservoir acidification construction design and optimization.

The invention discloses an online monitoring method for the energy efficiency of a drying part of a paper machine. The method comprises the following steps: based on material and energy conservation in the process of drying, establishing a quaternary partial differential equation set process model with paper temperature (Tp) and humidity (u) at a monitoring part of the drying part and temperature(Ta) and humidity (AHa) of air in a bag area at the monitoring part as unknown quantities; then using process data which are easily acquired in real time in the actual papermaking drying production process as known quantities, initial values and boundary conditions; and solving the quaternary partial differential equation set process model established in the invention to obtain real-time data of key technological parameters of the papermaking drying part, and then calculating the energy efficiency of the papermaking drying part so as to realize online monitoring of energy efficiency of the paper drying process. Thus, black-box operation is avoided, the operation condition of the papermaking drying part can be accurately mastered, and the method has important significance in guiding production adjustment and achieving energy conservation and emission reduction.

The present invention relates to a dynamic model solution method for a one-dimensional plug flow reactor with the feedstock of gas. The method comprises: starting from a mechanism model of a plug flowreactor (ideal tubular reactor), discretizing partial differential equations for describing the dynamics model into algebraic equations by using a finite difference method; converting the concentration in the model equation into a function of the temperature and gas molar flow by using a gas state equation; and by using simultaneous equations, solving to obtain distribution of the temperature andcomposition of the plug flow reactor with the space and time. The method disclosed by the present invention can be used for the calculation method for the ideal tubular reactor with the feedstock component of the gas phase, and the assumption that the gas volume flow must be set to a constant parameter in the previous solution process is overcome, so that the dynamic model solution result of thereactor is more accurate.

The soft robot modeling method comprises a white box model, a black box model and a gray box model. According to the white box model, starting from an internal mechanism of a material, a partial differential equation set is established by utilizing multidisciplinary knowledge of physics, chemistry, mechanics, electricity and the like to describe basic characteristics of the ionic EAP driver, and all parameters in the model have clear physical significance. According to the black box model, on the premise that the internal state change of the system is not considered, the model is directly established through the experiment identification technology according to the input and output relation of the system, and therefore an analytical solution of the model and a system transfer function are easily obtained. The grey box model is a model which is obtained by combining basic physical laws and experimental test data and utilizing a parameter identification technology and can reflect partial internal laws of the system.