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Upwind Advection One Interface Term Tool

First-order scalar upwind advective flux on a left-to-right interface normal; zero velocity selects the left state with zero flux.

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Description

Return a scalar upwind interface value and flux.

A simulation update combines supplied states, fluxes, forces and time conventions. Local integration and interface terms can be evaluated independently, while a full solver must also supply consistent fields, boundary conditions, conservation and convergence behavior.

Return a scalar upwind interface value and flux.

When to use this tool

Use Upwind Advection One Interface Term when checking one explicitly supplied integration, flux or lattice-population contribution.

How to use the tool and how it works

  1. Enter velocity, leftValue, rightValue. Use the units and conventions below.
  2. Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
  3. Read upwindValue, flux. Use the output convention below.

Return a scalar upwind interface value and flux. Choose leftValue when velocity >= 0, otherwise rightValue; flux = velocity*upwindValue.1

Input fieldMeaning and unitsAccepted input
velocityVelocityRequired. Finite number.
leftValueLeft ValueRequired. Finite number.
rightValueRight ValueRequired. Finite number.
Output fieldInterpretationReturned shape
upwindValueUpwind ValueRequired. Finite number.
fluxFluxRequired. Finite number.
json
{
  "input": {
    "velocity": 2,
    "leftValue": 3,
    "rightValue": 5
  },
  "output": {
    "upwindValue": 3,
    "flux": 6
  }
}

Limitations and assumptions

  • Zero velocity selects the left value but gives zero flux; no reconstruction, boundary condition or full transport solve occurs.
  • Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
  • Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Use and validate the complete numerical method with its state initialization, boundary conditions and physical model for a reliable simulation.

References

  1. Calculation and input contract: computational-physics/upwind-advection-one-interface-term — tool.io

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