485 results about "Partial differential equation" patented technology

The invention relates to a method of performing an oilfield operation of an oilfield having at least one wellsite, each wellsite having a wellbore penetrating a subterranean formation for extracting fluid from an underground reservoir therein. The method includes determining a time-step for simulating the reservoir using a reservoir model, the reservoir being represented as a plurality of gridded cells and being modeled as a multi-phase system using a plurality of partial differential equations, calculating a plurality of Courant-Friedrichs-Lewy (CFL) conditions of the reservoir model corresponding to the time-step, the plurality of CFL conditions being calculated for each of the plurality of gridded cells and comprising a temperature CFL condition, a composition CFL condition, and a saturation CFL condition calculated concurrently, simulating a first cell of the plurality of gridded cells using the reservoir model with an Implicit Pressure, Explicit Saturations (IMPES) system to obtain a first simulation result, the first cell having no CFL condition of the plurality of CFL conditions with a value greater than one, and simulating a second cell of the plurality of gridded cells using the reservoir model with a Fully Implicit Method (FIM) system to obtain a second simulation result, the second cell having at least one CFL condition of the plurality of CFL conditions with a value greater than one, and performing the oilfield operation based on the first and second simulation results.

The invention discloses a design method for a boundary control law of a flexible mechanical arm-based partial differential equation model. The design method comprises five steps of: 1, establishing a double-link flexible mechanical arm dynamic model; 2, decomposing the double-link flexible mechanical arm dynamic model; 3, designing an adaptive boundary control law; 4, verifying the global stability of a closed-loop system; and 5, finishing the design. By the design method, a condition that the frequency of joint angle movement is different from that of elastic oscillation is considered first, and a partial differential dynamic model is decomposed into a fast subsystem and a slow subsystem by a singular perturbation method; a slow adaptive boundary control law is designed on the slow subsystem, so that a joint motor can move to an expected position; a fast adaptive boundary control law is designed on the fast subsystem to inhibit the elastic oscillation; and the fast and slow subsystems form a hybrid controller to control the joint angle and oscillation of a double-link flexible mechanical arm and ensure the global stability of the closed-loop system.

Fast reconstruction methods are provided for 3D time-of-flight (TOF) positron emission tomography (PET), based on 2D data re-binning. Starting from pre-corrected 3D TOF data, a re-binning algorithm estimates for each transaxial slice the 2D TOF sinogram. The re-binned sinograms can then be reconstructed using any algorithm for 2D TOF reconstruction. A TOF-FORE (Fourier re-binning of TOF data) algorithm is provided as an approximate re-binning algorithm obtained by extending the Fourier re-binning method for non-TOF data. In addition, two partial differential equations are identified that must be satisfied by consistent 3D TOF data, and are used to derive exact re-binning algorithms and to characterize the degree of the approximation in TOF-FORE. Numerical simulations demonstrate that TOF-FORE is more accurate than two different TOF extensions of the single-slice re-binning method, and suggest that TOF-FORE will be a valuable tool for practical TOF PET in the range of axial apertures and time resolutions typical of current scanners.

The subject invention pertains to a method of image intensity correction. The subject invention can utilize extrapolation for image intensity correction. The use of extrapolation can reduce the artifacts during intensity correction as compared to traditional methods of intensity correction. The extrapolation can be combined with, for example, homomorphic filtering methods, parametric estimation techniques, wavelet based method, and/or Gaussian smooth method, in order to reduce the artifacts generated by these methods and improve the quality of correction. The implementation of image extrapolation in accordance with a specific embodiment can utilize closest point method. The subject method can also use adaptive smoothing for image intensity correction. In an embodiment, the use of gradient weighted smoothing method can reduce, or eliminate, over-smoothing of bright spot regions. In a specific embodiment, the subject method can utilize gradient weighted partial differential equation (PDE) smoothing.

The invention discloses a reverse design method for an impeller of a centrifugal pump, which comprises the following steps: according to a given impeller axial plane, a blade in a three-dimensional space can be actually expressed as X=X(z(u, v), r(u, v), theta(u, v)), the (z(u, v), r(u, v)) has been determined when a streamline of the impeller axial plane is given, and the space modeling of the blade can be determined by determining the theta(u, v) on the impeller axial plane. The reverse design method is characterized in that the reverse design method transforms a geometric design problem of the blade of the centrifugal pump into a boundary value problem of a partial differential equation to solve under the condition of the given impeller axial plane of the centrifugal pump. The reverse design method overcomes a lot of disadvantages such as the definition and modification of geometrical shape of the blade in the prior design method, can realize the parametric design of the blade, overcome the defects existing when a fussy two-dimensional form drawing is used for showing three-dimensional twisted blades in the prior method, can closely combine the hydraulic design of hydraulic machinery, three-dimensional solid modeling and the CFD analysis of flow field, and realize the quick and accurate solving of the reverse problem of the blade.

The invention relates to a joint estimation method of a state of charge (SOC) and a state of health (SOH) of a power battery system based on an electrochemical model. The method comprises the steps of establishing a pseudo two-dimensional electrochemical model correlation mathematical equation based on an electrochemical correlation theory, performing dimensionality reduction processing and calculation solution on a complicated partial differential equation by a finite analysis method and a numerical calculation method, allowing an open circuit potential of an electrode to be equivalent to open circuit voltage of a battery, establishing a capacity-surface SOC-EOCV three-dimensional response surface, extracting and establishing a degradation path graph of a battery performance degradation characteristic parameter by an intelligent optimization algorithm based on battery ageing test data, and finally realizing estimation of the SOH of the power battery based on the degradation path graph and realizing estimation of the SOC of the power battery based on concentration distribution and change rules of lithium ions in the battery.

The invention discloses an evaluation method for unconventional reservoir volume transformation multi-pore media productivity contribution. The evaluation method comprises the following steps that firstly, based on the principle of effective stress and flow characteristics of a transformation zone, and a fluid-solid coupling mathematical model of interaction between a geotechnical deformation field (stress field) and a fluid flow field (seepage field) of the unconventional reservoirs is established; then a perfectly coupled method solution of the seepage field and the stress field is realizedby solving a fluid-solid perfectly coupled system of partial differential equations in a general formula mode; and finally, fluid-solid coupling interactions under different combinations of pore mediaare simulated, and the contribution ratio of three systems of base materials, natural cracks and grid cracks to the cumulative production of a volume transformation well is obtained. A set of evaluation method for unconventional reservoir volume transformation multi-pore media productivity contribution is established eventually. The evaluation method for unconventional reservoir volume transforming multi-pore media productivity contribution has the advantages that the model factor consideration is comprehensive, the evaluation method is simple and results are quantifiable, an oil and gas field can be guided timely to be subjected to development measure adjustment and comprehensive management, and a theoretical basis and technical support are provided to the unconventional reservoir to realize economic recovery.

The invention provides an image denoising method, which comprises the following steps: designing a functional E (u); obtaining a corresponding Euler equation according to the functional E (u); deducing and solving a discrete mathematical model according to the Euler equation, wherein the discrete mathematical model is used for smoothening an image and strengthening detained information; inputting an image u0; carrying out iterative denoising for the input image u0 through the discrete mathematical model, thereby obtaining a denoised image u (i, j); removing spots on the denoised image u (i, j); and outputting an image which spots are removed. The image denoising method provided by the invention overcomes the 'block effect' introduced in the denoising method based on the second-order partial differential equation, and not only denoise the image, but also increases the contrast, thereby maintaining the detailed information of the texture and making the visual effect of the image more vivid and natural.

A method of cloth simulation using a constrainable multigrid is provided. The method includes steps of: calculating a change of geometry of the mesh of nodes at a plurality of time steps using a multigrid method by solving a time-varying partial differential equation at multiple resolutions or levels; providing a hierarchical mesh through restriction or coarsening by down-sampling from level m to m−1 or prolongation or interpolation by up-sampling from level m to m+1; transferring soft constraints between different hierarchical levels using a damper-based constraint method; updating the position vector x and the velocity vector v of the mesh nodes; and displaying an updated state of the mesh of nodes using updated position vector x and velocity vector v on a display.

The invention discloses an RVM (relevant vector machine) method for RMW (radius of maximum wind) and typhoon eye dimension modeling, in order to establish a model of eye typhoon RMW and typhoon eye dimension based on the RVM. Hereto, according to the invention, the method comprises the following steps of: estimating the RMW through calculating the distance between the coldest temperature point at the top of the cloud and the warmest point within an eye wall on a typhoon cloud picture; dividing the typhoon eye based on patial differential equation, and measuring the dimension of the typhoon eye by the perimeter of the eye wall; and finally establishing the model of the RMW and the typhoon eye dimension based on the RVM, and comparing with the modeling methods of SVM (support vector machine), linear regression, radial basis function neural network and the like. Because the technical scheme provided by the invention is adopted, a good modeling result can be obtained; and compared with other modeling methods, the RVM-based modeling effect has much smaller errors, so that the inner core structure of a wind field at the low layer of typhoon can be depicted favorably.

The invention has opened a free curved surface reflection design procedures and use of one small projection installment lighting system. Free curved surface reflection of light implement design procedures is adopted law of refection , illuminance formula and energy conservation , according to the luminescence characteristic of lamp-house and needed target the balancing illumination, infers a group of partial differential equations, used differences law to find the solution, whose numerical value solution is to be a free curved surface reflection of light implement shape data , the specific target uniform rectangular lighting formed by the free curved surface reflection's refection to the photosource, can be applied to small LED light source for projection Lighting System.Its main merits are: (1) calculation time is short, only a few minutes that will be required for a free curved surface reflection; (2) the utilization of light energy is high; (3) the degree of illumination uniformity is good; (4) applying in the small projection installment of lighting system, will enable the system structure to be more compact.

The invention belongs to the technical field related to structure topological optimization design, and discloses an efficient structure frequency response topological optimization method. The method comprises the following steps that: (1) decoupling two coupling variables including time and space in a standard level set function in a dynamic model of which the structure is to be optimized, and meanwhile, expressing the level set function related to time as a matrix product form; (2) converting a partial differential equation of the time-related level set function into an ordinary differential equation so as to obtain a new linear system, and solving to obtain the time-related level set function; (3) carrying out finite element analysis on a macrostructure so as to calculate a target function and a constraint function of a structure optimization problem; and (4) calculating the sensitivity, which relates to a design variable of the target function and the constraint function obtained in the (3), and judging whether the target function is convergent or not after the design variable is updated. By use of the method, a discrete wavelet transform technology is adopted to carry out recompression on an interpolation matrix, efficiency is improved, and cost is lowered.

The invention discloses a progressive additional lens and a preparation method thereof. According to the prior art, on the basis of acquiring initial rise data of an additional lens surface shape, an optimization method for acquiring small-area local correction surface rise by solving a partial differential equation introducing an optimization function is established. The optimization function is that an optimization factor is added into a lens surface shape average curvature distribution function, the lens surface shape rise is finally obtained by regulating the optimization factor and performing multiple iteration, and the lens is processed, so that the width of an area with the astigmatism less than or equal to 0.25 dioptry in a middle transition area corresponding to the provided lens is increased by more than or equal to 1mm, and the optical property in an effective visual area is not changed basically; therefore, the initial design parameters and the optical property of the lens are kept not changed, the dioptry and the astigmatism distribution of the lens better meet the requirements of wearers.

A method, program and apparatus for generating partial differential equations for perspective corrected texture coordinates in a computer graphics display are provided. The present invention comprises calculating texture coordinates for four adjacent pixels and then determining the differences between the coordinates. A perspective correction factor is then calculated, which is multiplied by each coordinate difference.