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112 lines
3 KiB
Markdown
112 lines
3 KiB
Markdown
# Heat-2D Adapter
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This repository is the 2D diffusion / dissipative-residue sandbox for the pressure-cavitation-vibration model catalog.
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## Core role
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```text
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shock / pressure / vibration / combustion / friction event
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-> deposited scalar residue
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-> 2D diffusion
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-> measurable afterimage field
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```
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In the broader stack:
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```text
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Burgers handles shock smoothing.
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heat-2D handles deposited residue.
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```
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## Native PDE
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The upstream README defines the supported PDE family as:
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```math
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\partial_t u = \nabla\cdot(\alpha\nabla u)+f
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```
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where `u(x,y,t)` is the diffusive variable, `alpha(x,y)` is a space-dependent diffusivity, and `f(x,y,t)` is a source term.
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For catalog integration, reinterpret these as:
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| Field | Catalog interpretation |
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|---|---|
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| `u` | residual field: heat, deposited shock energy, vibration residue, or pressure-afterimage proxy |
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| `alpha` | material / geometry-dependent diffusivity |
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| `f` | source term from cavitation, combustion, friction, impact, or acoustic deposit |
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| boundary conditions | heat/pressure residue sinks, walls, insulation, or imposed driving surfaces |
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## Adapter definition
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```math
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X_{heat2D}=(u,\alpha,f,\Omega,\partial\Omega,\Delta x,\Delta y,\Delta t,B)
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```
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```math
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\alpha_{heat2D}:X_{heat2D}\rightarrow U_T(x,y,t)
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```
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The adapter is admissible when:
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1. boundary conditions are explicit,
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2. source units are documented,
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3. geometry masks are kept separate from solver logic,
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4. stability requirements are checked for explicit integration,
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5. implicit or Crank-Nicolson runs include linear-solver receipt metadata.
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## Candidate source projections
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### Cavitation collapse deposit
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```math
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f(x,y,t)=E_{shock}\exp\left(-\frac{(x-x_0)^2+(y-y_0)^2}{2\sigma_s^2}\right)\delta(t-t_0)
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```
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### Rocket cooling proxy
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```math
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\partial_t T=\nabla\cdot(\alpha\nabla T)+q''_{combustion}-q''_{coolant}
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```
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### Passive fluidic residue map
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Use `alpha(x,y)` to encode channels, walls, pockets, and damping zones:
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```math
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\partial_t u=\nabla\cdot(\alpha(x,y)\nabla u)+f
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```
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### Burgers dissipative afterimage
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```math
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f_{diss}(x,y,t)=\lambda\nu(\partial_x U)^2
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```
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## Minimal tests
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| Test | Purpose | Expected behavior |
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|---|---|---|
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| point impulse | pure diffusion sanity check | radial spread, decaying max |
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| line source | shock-front residue proxy | front thickens like sqrt(t) |
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| geometry mask | passive fluidic damping test | pockets and channels alter residue storage |
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| cooling channel | rocket wall proxy | stable gradient under balanced source/sink |
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## Failure modes
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| Failure | Meaning |
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| oscillation in pure explicit heat solve | timestep instability |
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| negative values from nonnegative initial/source field | instability or source bug |
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| energy growth with no source | boundary/source accounting error |
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| claiming CFD from diffusion | category error |
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## Scope warning
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This repository should not be treated as a full Navier-Stokes, cavitation, rocket-engine, or acoustic solver.
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Its correct role is narrower and more useful:
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```text
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Given a source event, what dissipative residue field remains?
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```
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