Optimal Pressure-Projection Method For Incompressible Transient And Steady-State Navier-Stokes Equations

    公开(公告)号:US20170364615A1

    公开(公告)日:2017-12-21

    申请号:US15185707

    申请日:2016-06-17

    CPC classification number: G06F17/5009 G06F17/5018 G06F2217/16

    Abstract: Embodiments of the present invention simulate a real-world system by first generating a time dependent system of equations that represents the real-world system where the time dependent system of equations has a defined constraint. Next, the constraint is de-coupled from the time-dependent system of equations using a matrix representing an approximation of physics of the real-world system, the de-coupling generating a first system of equations representing the constraint and a second system of equations representing physics of the real-world system. In turn, the generated first and second systems of equations are solved and the real-world system is automatically simulated by generating a simulation using results from solving the first and second systems of equations.

    Optimal pressure-projection method for incompressible transient and steady-state navier-stokes equations

    公开(公告)号:US10599879B2

    公开(公告)日:2020-03-24

    申请号:US15185707

    申请日:2016-06-17

    Abstract: Embodiments of the present invention simulate a real-world system by first generating a time dependent system of equations that represents the real-world system where the time dependent system of equations has a defined constraint. Next, the constraint is de-coupled from the time-dependent system of equations using a matrix representing an approximation of physics of the real-world system, the de-coupling generating a first system of equations representing the constraint and a second system of equations representing physics of the real-world system. In turn, the generated first and second systems of equations are solved and the real-world system is automatically simulated by generating a simulation using results from solving the first and second systems of equations.

    Convergence estimation of non-linear PDE and linear solvers

    公开(公告)号:US10303825B2

    公开(公告)日:2019-05-28

    申请号:US14981263

    申请日:2015-12-28

    Abstract: A method, according to an embodiment, provides a simulation of a physical real-world system, by first generating a system of equations that includes a discrete representation of the real-world system being simulated. Next, the real-world system is simulated. In simulating the system, a user specified tolerance of a solution of the system of equations is obtained. Then, the system of equations is iteratively solved until a solution to the system of equations for a given iteration is within the user specified tolerance of the solution of the system of equations for approximately infinite iterations. In such an embodiment, the solution to the system of equations for the given iteration is determined to be within the user specified tolerance using an experimentally determined constant, an estimate of a minimum eigenvalue of the system of equations for the given iteration, and a residual of the system of equations for the given iteration.

    Convergence Estimation OF Non-Linear PDE And Linear Solvers

    公开(公告)号:US20170185707A1

    公开(公告)日:2017-06-29

    申请号:US14981263

    申请日:2015-12-28

    CPC classification number: G06F17/5018 G06F17/12 G06F17/5009

    Abstract: A method, according to an embodiment, provides a simulation of a physical real-world system, by first generating a system of equations that includes a discrete representation of the real-world system being simulated. Next, the real-world system is simulated. In simulating the system, a user specified tolerance of a solution of the system of equations is obtained. Then, the system of equations is iteratively solved until a solution to the system of equations for a given iteration is within the user specified tolerance of the solution of the system of equations for approximately infinite iterations. In such an embodiment, the solution to the system of equations for the given iteration is determined to be within the user specified tolerance using an experimentally determined constant, an estimate of a minimum eigenvalue of the system of equations for the given iteration, and a residual of the system of equations for the given iteration.

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