Class TimeIntegrator

java.lang.Object
neqsim.process.equipment.pipeline.twophasepipe.numerics.TimeIntegrator
All Implemented Interfaces:
Serializable
public class TimeIntegrator extends Object implements Serializable
Time integration methods for the two-fluid transient pipe model.

Provides explicit time stepping algorithms with CFL-based adaptive time step control. The primary method is the classical 4th-order Runge-Kutta (RK4) scheme.

RK4 Algorithm

For dU/dt = R(U):

  • k1 = R(U^n)
  • k2 = R(U^n + 0.5*dt*k1)
  • k3 = R(U^n + 0.5*dt*k2)
  • k4 = R(U^n + dt*k3)
  • U^{n+1} = U^n + dt/6 * (k1 + 2*k2 + 2*k3 + k4)

CFL Condition

The time step is limited by: dt ≤ CFL * dx / (|v| + c) where c is the sound speed and CFL is typically 0.5-0.9 for explicit schemes.

Version:
1.0
Author:
Even Solbraa
See Also:

  • Field Details

    • serialVersionUID

      private static final long serialVersionUID
      See Also:

    • method

      private TimeIntegrator.Method method
      Current integration method.

    • cflNumber

      private double cflNumber
      CFL number for time step control (0 < CFL < 1).

    • minTimeStep

      private double minTimeStep
      Minimum allowed time step (s).

    • maxTimeStep

      private double maxTimeStep
      Maximum allowed time step (s).

    • currentTime

      private double currentTime
      Current simulation time (s).

    • currentDt

      private double currentDt
      Current time step (s).

  • Constructor Details

    • TimeIntegrator

      public TimeIntegrator()
      Default constructor.

    • TimeIntegrator

      public TimeIntegrator(TimeIntegrator.Method method)
      Constructor with method selection.
      Parameters:
      method - Integration method

  • Method Details

    • step

      public double[][] step(double[][] U, TimeIntegrator.RHSFunction rhs, double dt)
      Advance solution by one time step using selected method.
      Parameters:
      U - Current state [nCells][nVars]
      rhs - Right-hand side function
      dt - Time step
      Returns:
      Updated state at t + dt

    • stepEuler

      public double[][] stepEuler(double[][] U, TimeIntegrator.RHSFunction rhs, double dt)
      Forward Euler method (first-order).

      U^{n+1} = U^n + dt * R(U^n)

      Parameters:
      U - Current state
      rhs - Right-hand side function
      dt - Time step
      Returns:
      Updated state

    • stepRK2

      public double[][] stepRK2(double[][] U, TimeIntegrator.RHSFunction rhs, double dt)
      Second-order Runge-Kutta (Heun's method).
      Parameters:
      U - Current state
      rhs - Right-hand side function
      dt - Time step
      Returns:
      Updated state

    • stepRK4

      public double[][] stepRK4(double[][] U, TimeIntegrator.RHSFunction rhs, double dt)
      Classical 4th-order Runge-Kutta.
      Parameters:
      U - Current state
      rhs - Right-hand side function
      dt - Time step
      Returns:
      Updated state

    • stepSSPRK3

      public double[][] stepSSPRK3(double[][] U, TimeIntegrator.RHSFunction rhs, double dt)
      Strong Stability Preserving RK3 (Shu-Osher).

      Maintains TVD property, good for problems with shocks.

      Parameters:
      U - Current state
      rhs - Right-hand side function
      dt - Time step
      Returns:
      Updated state

    • calcStableTimeStep

      public double calcStableTimeStep(double maxWaveSpeed, double dx)
      Calculate stable time step based on CFL condition.
      Parameters:
      maxWaveSpeed - Maximum wave speed in the domain (|v| + c)
      dx - Minimum cell size
      Returns:
      Stable time step

    • calcTwoFluidTimeStep

      public double calcTwoFluidTimeStep(double[] gasVelocities, double[] liquidVelocities, double[] gasSoundSpeeds, double[] liquidSoundSpeeds, double dx)
      Calculate stable time step for two-fluid system.
      Parameters:
      gasVelocities - Gas velocities at each cell (m/s)
      liquidVelocities - Liquid velocities at each cell (m/s)
      gasSoundSpeeds - Gas sound speeds at each cell (m/s)
      liquidSoundSpeeds - Liquid sound speeds at each cell (m/s)
      dx - Cell size (m)
      Returns:
      Stable time step

    • advanceTime

      public void advanceTime(double dt)
      Advance current time by dt.
      Parameters:
      dt - Time step taken

    • addArrays

      private double[][] addArrays(double[][] A, double[][] B)
      Add two 2D arrays element-wise.
      Parameters:
      A - First array
      B - Second array
      Returns:
      A + B

    • scaleArray

      private double[][] scaleArray(double[][] A, double s)
      Scale a 2D array by a scalar.
      Parameters:
      A - Array
      s - Scalar
      Returns:
      s * A

    • getMethod

      public TimeIntegrator.Method getMethod()
      Get integration method.
      Returns:
      Current method

    • setMethod

      public void setMethod(TimeIntegrator.Method method)
      Set integration method.
      Parameters:
      method - New method

    • getCflNumber

      public double getCflNumber()
      Get CFL number.
      Returns:
      CFL number

    • setCflNumber

      public void setCflNumber(double cflNumber)
      Set CFL number.
      Parameters:
      cflNumber - New CFL number (0 < CFL < 1)

    • getMinTimeStep

      public double getMinTimeStep()
      Get minimum time step.
      Returns:
      Minimum time step (s)

    • setMinTimeStep

      public void setMinTimeStep(double minTimeStep)
      Set minimum time step.
      Parameters:
      minTimeStep - Minimum time step (s)

    • getMaxTimeStep

      public double getMaxTimeStep()
      Get maximum time step.
      Returns:
      Maximum time step (s)

    • setMaxTimeStep

      public void setMaxTimeStep(double maxTimeStep)
      Set maximum time step.
      Parameters:
      maxTimeStep - Maximum time step (s)

    • getCurrentTime

      public double getCurrentTime()
      Get current simulation time.
      Returns:
      Current time (s)

    • setCurrentTime

      public void setCurrentTime(double currentTime)
      Set current simulation time.
      Parameters:
      currentTime - Current time (s)

    • getCurrentDt

      public double getCurrentDt()
      Get current time step.
      Returns:
      Current time step (s)

    • reset

      public void reset()
      Reset integrator state.