Class MUSCLReconstructor

java.lang.Object
neqsim.process.equipment.pipeline.twophasepipe.numerics.MUSCLReconstructor
All Implemented Interfaces:
Serializable
public class MUSCLReconstructor extends Object implements Serializable
MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) reconstruction.

Provides second-order spatial accuracy by reconstructing cell-interface values from cell-average values using slope limiters to prevent spurious oscillations near discontinuities.

Reconstruction Formula

For a cell i with value U_i:

  • Left interface value: U_{i+1/2,L} = U_i + 0.5 * φ(r) * (U_i - U_{i-1})
  • Right interface value: U_{i-1/2,R} = U_i - 0.5 * φ(r) * (U_{i+1} - U_i)

where φ(r) is the slope limiter and r is the ratio of consecutive gradients.

Available Limiters

  • Minmod: Most diffusive, very robust
  • Van Leer: Good balance of accuracy and stability
  • Van Albada: Smooth limiter, good for smooth solutions
  • Superbee: Least diffusive, can be oscillatory
  • MC (Monotonized Central): Between minmod and superbee

References

  • van Leer, B. (1979) - Towards the ultimate conservative difference scheme V.
  • Sweby, P.K. (1984) - High resolution schemes using flux limiters
Version:
1.0
Author:
Even Solbraa
See Also:

  • Field Details

  • Constructor Details

    • MUSCLReconstructor

      public MUSCLReconstructor()
      Default constructor using Van Leer limiter.

    • MUSCLReconstructor

      public MUSCLReconstructor(MUSCLReconstructor.SlopeLimiter limiter)
      Constructor with specified limiter.
      Parameters:
      limiter - Slope limiter type

  • Method Details

    • reconstruct

      public MUSCLReconstructor.ReconstructedPair reconstruct(double uLeft, double uCenter, double uRight, double uFarRight)
      Reconstruct interface values between cells i and i+1.
      Parameters:
      uLeft - Value at cell i-1 (or i for boundary)
      uCenter - Value at cell i
      uRight - Value at cell i+1
      uFarRight - Value at cell i+2 (or i+1 for boundary)
      Returns:
      Reconstructed left and right states at interface i+1/2

    • reconstructArray

      public MUSCLReconstructor.ReconstructedPair[] reconstructArray(double[] u)
      Reconstruct interface values for an array of cell values.

      Returns arrays of left and right states at each interface.

      Parameters:
      u - Cell-average values [0..n-1]
      Returns:
      Array of reconstructed pairs at interfaces [0..n-2]

    • calcLimitedSlope

      public double calcLimitedSlope(double deltaLeft, double deltaRight)
      Calculate limited slope using current limiter.
      Parameters:
      deltaLeft - Left difference (U_i - U_{i-1})
      deltaRight - Right difference (U_{i+1} - U_i)
      Returns:
      Limited slope

    • calcLimiter

      public double calcLimiter(double r)
      Calculate slope limiter value φ(r).
      Parameters:
      r - Gradient ratio
      Returns:
      Limiter value φ

    • minmod

      public double minmod(double r)
      Minmod limiter: φ(r) = max(0, min(1, r)).

      Most diffusive limiter, very robust for shocks.

      Parameters:
      r - Gradient ratio
      Returns:
      Limiter value

    • vanLeer

      public double vanLeer(double r)
      Van Leer limiter: φ(r) = (r + |r|) / (1 + |r|).

      Smooth limiter with good balance of accuracy and stability.

      Parameters:
      r - Gradient ratio
      Returns:
      Limiter value

    • vanAlbada

      public double vanAlbada(double r)
      Van Albada limiter: φ(r) = (r² + r) / (r² + 1).

      C1 continuous, good for smooth solutions.

      Parameters:
      r - Gradient ratio
      Returns:
      Limiter value

    • superbee

      public double superbee(double r)
      Superbee limiter: φ(r) = max(0, min(2r, 1), min(r, 2)).

      Least diffusive, compresses discontinuities but can overshoot.

      Parameters:
      r - Gradient ratio
      Returns:
      Limiter value

    • mc

      public double mc(double r)
      MC (Monotonized Central) limiter: φ(r) = max(0, min(2, 2r, (1+r)/2)).

      Between minmod and superbee in diffusivity.

      Parameters:
      r - Gradient ratio
      Returns:
      Limiter value

    • minmod3

      public double minmod3(double a, double b, double c)
      Classic minmod function for three arguments.
      Parameters:
      a - First value
      b - Second value
      c - Third value
      Returns:
      Minmod result

    • getLimiterType

      public MUSCLReconstructor.SlopeLimiter getLimiterType()
      Get current limiter type.
      Returns:
      Current slope limiter

    • setLimiterType

      public void setLimiterType(MUSCLReconstructor.SlopeLimiter limiterType)
      Set limiter type.
      Parameters:
      limiterType - New slope limiter

    • isSecondOrder

      public boolean isSecondOrder()
      Check if reconstruction is second-order.
      Returns:
      true if using a limiter (second-order)