forked from 1b-agent/fieldcraft-upstream
verification: series-resistance heat flow across a tie (#358)
Co-Authored-By: Claude Opus 5.5 <[email protected]> Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
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jyvikoandClaude Opus 5.5 authored and Irakli Kourtis committed
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{
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"title": "Heat through a tie: two blocks of conductivities 10 and 40 with non-matching meshes, 20 and 100 at the ends",
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"kind": "theory",
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"source": "Series thermal resistances: steady one-dimensional conduction through two layers in perfect contact, T_i = (k1 T0 + k2 T1)/(k1 + k2) and q = ΔT/(L1/k1 + L2/k2) (F. P. Incropera, D. P. DeWitt, Fundamentals of Heat and Mass Transfer, §3.1, the composite wall). A linear field in each layer is the exact discrete solution, and the dual mortar tie reproduces a linear temperature across non-matching meshes",
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"quantities": [
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{
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"id": "t_interface",
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"quantity": "T at the tied secondary node (0.5, 0.5, 1)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Heat",
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"at": [
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[
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0.5,
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0.5,
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1.0
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]
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]
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},
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"pointer": "/nodes/0/temperature"
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},
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"value": 84.0,
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"tolerance": {
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"relative": 1e-09
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},
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"reason": "exact discrete solution: linear in each block, and the tie holds the interface temperature for non-matching meshes"
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},
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{
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"id": "t_lower",
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"quantity": "T in the lower block at (0, 0, 0.5)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Heat",
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"at": [
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[
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0.0,
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0.0,
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0.5
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]
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]
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},
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"pointer": "/nodes/0/temperature"
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},
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"value": 52.0,
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"tolerance": {
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"relative": 1e-09
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},
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"reason": "exact discrete solution: linear in each block, and the tie holds the interface temperature for non-matching meshes"
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},
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{
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"id": "t_upper",
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"quantity": "T in the upper block at (1, 1, 1.5)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Heat",
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"at": [
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[
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1.0,
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1.0,
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1.5
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]
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]
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},
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"pointer": "/nodes/0/temperature"
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},
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"value": 92.0,
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"tolerance": {
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"relative": 1e-09
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},
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"reason": "exact discrete solution: linear in each block, and the tie holds the interface temperature for non-matching meshes"
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},
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{
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"id": "q_lower",
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"quantity": "heat flux q_z at (0, 0, 0.5)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Heat",
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"at": [
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[
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0.0,
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0.0,
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0.5
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]
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]
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},
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"pointer": "/nodes/0/heat_flux/2"
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},
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"value": -640.0,
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"tolerance": {
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"relative": 1e-09
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},
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"reason": "the heat flow ΔT/(1/k1 + 1/k2) = 640 per unit area, −k ∂T/∂z uniform in each block"
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},
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{
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"id": "q_upper",
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"quantity": "heat flux q_z at (1, 1, 1.5)",
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"measure": {
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"command": "solve.probe",
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"params": {
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"step": "Heat",
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"at": [
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[
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1.0,
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1.0,
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1.5
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]
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]
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},
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"pointer": "/nodes/0/heat_flux/2"
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},
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"value": -640.0,
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"tolerance": {
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"relative": 1e-09
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},
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"reason": "the same heat flow crosses the tie: nothing is lost at the interface"
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}
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]
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}
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@@ -0,0 +1,25 @@
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{
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"note": "FieldCraft's accepted results for this case, written by `cargo xtask oracle --bless`. A result outside its band fails CI.",
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"values": {
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"q_lower": {
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"band": 6.400000000000002e-7,
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"value": -640.0000000000002
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},
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"q_upper": {
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"band": 6.400000000000015e-7,
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"value": -640.0000000000015
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},
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"t_interface": {
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"band": 8.400000000000002e-8,
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"value": 84.00000000000001
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},
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"t_lower": {
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"band": 5.2000000000000035e-8,
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"value": 52.000000000000036
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},
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"t_upper": {
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"band": 9.200000000000008e-8,
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"value": 92.00000000000007
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}
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}
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}
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@@ -0,0 +1,19 @@
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[
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{"command": "mesh.block", "params": {"body": "Lower", "kind": "hex8", "corners": [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0], [0, 0, 1], [1, 0, 1], [1, 1, 1], [0, 1, 1]], "divisions": [3, 3, 2], "faces": {"1": "bottom", "2": "top"}, "bias": [2.0, 0.6, 1.0]}},
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{"command": "mesh.block", "params": {"body": "Upper", "kind": "hex8", "corners": [[0, 0, 1], [1, 0, 1], [1, 1, 1], [0, 1, 1], [0, 0, 2], [1, 0, 2], [1, 1, 2], [0, 1, 2]], "divisions": [2, 2, 2], "faces": {"1": "bottom", "2": "top"}, "merge": 0}},
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{"command": "model.set.create", "params": {"name": "lower", "geometry": [{"body": "Lower"}]}},
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{"command": "model.set.create", "params": {"name": "upper", "geometry": [{"body": "Upper"}]}},
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{"command": "model.set.create", "params": {"name": "lower_top", "geometry": [{"body": "Lower", "face": "top"}]}},
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{"command": "model.set.create", "params": {"name": "upper_bottom", "geometry": [{"body": "Upper", "face": "bottom"}]}},
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{"command": "model.set.create", "params": {"name": "cold", "geometry": [{"body": "Lower", "face": "bottom"}]}},
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{"command": "model.set.create", "params": {"name": "hot", "geometry": [{"body": "Upper", "face": "top"}]}},
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{"command": "model.material.create", "params": {"name": "Low", "elastic": {"type": "isotropic", "young": 1000.0, "poisson": 0.3}, "thermal": {"conductivity": 10.0}}},
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{"command": "model.material.create", "params": {"name": "High", "elastic": {"type": "isotropic", "young": 1000.0, "poisson": 0.3}, "thermal": {"conductivity": 40.0}}},
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{"command": "model.section.create", "params": {"name": "lower", "set": "lower", "material": "Low", "kind": {"type": "solid"}}},
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{"command": "model.section.create", "params": {"name": "upper", "set": "upper", "material": "High", "kind": {"type": "solid"}}},
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{"command": "interaction.tie", "params": {"name": "glue", "main": "lower_top", "secondary": "upper_bottom"}},
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{"command": "model.boundary_condition.create", "params": {"name": "cold", "type": "temperature", "target": {"set": "cold"}, "value": 20.0}},
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{"command": "model.boundary_condition.create", "params": {"name": "hot", "type": "temperature", "target": {"set": "hot"}, "value": 100.0}},
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{"command": "model.step.create", "params": {"name": "Heat", "procedure": {"type": "heat_transfer"}, "boundary_conditions": ["cold", "hot"], "loads": []}},
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{"command": "solve.heat", "params": {"step": "Heat"}, "id": "heat"}
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]
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