L2 norm

conf/config.yaml

@@ -8,6 +8,7 @@
 defaults:
   - problem: ldc
   - solver: fv
+  - validation: fv
   - mlflow: local
   - machine: local
   - _self_

conf/experiment/fv_validation.yaml

@@ -0,0 +1,26 @@
+# @package _global_
+# FV Solver validation against Ghia benchmark
+# Usage: uv run python run_solver.py +experiment=fv_validation
+#        uv run python run_solver.py -m +experiment=fv_validation  (sweep all)
+
+defaults:
+  - override /solver: fv
+
+# MLflow experiment (shared with spectral_validation)
+experiment_name: LDC-Validation
+# Parent run name - use same name across fv/spectral to group them
+sweep_name: validation
+
+# Validation grid sizes and Reynolds numbers
+N: 32
+Re: 100
+tolerance: 1.0e-6
+max_iterations: 10000
+
+hydra:
+  sweeper:
+    params:
+      N: 32,64
+      Re: 100
+
+

conf/experiment/validation/convergence/fv-regu-1000.yaml

@@ -0,0 +1,21 @@
+# @package _global_
+# Convergence test - FV solver reference with Saad regularization at Re=1000
+# N=128 as reference solution for spectral convergence
+
+defaults:
+  - override /solver: fv
+  - override /validation: fv-regu
+
+# MLflow experiment
+experiment_name: LDC-Convergence
+sweep_name: regu-Re1000
+
+# Use Saad/polynomial corner treatment for regularized problem
+solver:
+  corner_treatment: saad
+
+hydra:
+  sweeper:
+    params:
+      Re: 1000
+      N: 128

conf/experiment/validation/convergence/fv-regu-400.yaml

@@ -0,0 +1,21 @@
+# @package _global_
+# Convergence test - FV solver reference with Saad regularization at Re=400
+# N=128 as reference solution for spectral convergence
+
+defaults:
+  - override /solver: fv
+  - override /validation: fv-regu
+
+# MLflow experiment
+experiment_name: LDC-Convergence
+sweep_name: regu-Re400
+
+# Use Saad/polynomial corner treatment for regularized problem
+solver:
+  corner_treatment: saad
+
+hydra:
+  sweeper:
+    params:
+      Re: 400
+      N: 128

conf/experiment/validation/convergence/spectral-regu-1000.yaml

@@ -0,0 +1,21 @@
+# @package _global_
+# Convergence test - Spectral solver with Saad regularization at Re=1000
+# Sweep over N values with polynomial corner treatment
+
+defaults:
+  - override /solver: spectral/fsg
+  - override /validation: fv-regu
+
+# MLflow experiment
+experiment_name: LDC-Convergence
+sweep_name: regu-Re1000
+
+# Use Saad/polynomial corner treatment for regularized problem
+solver:
+  corner_treatment: saad
+
+hydra:
+  sweeper:
+    params:
+      Re: 1000
+      N: 48, 64, 80, 96, 112, 128

conf/experiment/validation/convergence/spectral-regu-400.yaml

@@ -0,0 +1,21 @@
+# @package _global_
+# Convergence test - Spectral solver with Saad regularization at Re=400
+# Sweep over N values with polynomial corner treatment
+
+defaults:
+  - override /solver: spectral/fsg
+  - override /validation: fv-regu
+
+# MLflow experiment
+experiment_name: LDC-Convergence
+sweep_name: regu-Re400
+
+# Use Saad/polynomial corner treatment for regularized problem
+solver:
+  corner_treatment: saad
+
+hydra:
+  sweeper:
+    params:
+      Re: 400
+      N: 24, 32, 40, 48, 56, 64

conf/experiment/validation/convergence/spectral.yaml

@@ -0,0 +1,20 @@
+# @package _global_
+# Ghia validation - Spectral solvers
+# Sweeps over SG, FSG, VMG, FMG solvers at N=15
+
+defaults:
+  - override /solver: spectral/sg
+
+# MLflow experiment
+experiment_name: LDC-Validation
+sweep_name: convergence-rate-2
+
+# Validation parameters
+
+hydra:
+  sweeper:
+    params:
+      # Sweep over spectral solver types
+      solver: spectral/fsg #,spectral/fsg
+      Re: 1000
+      N: 80, 90, 100, 110, 120, 130, 140

conf/experiment/validation/ghia/fv.yaml

@@ -13,5 +13,5 @@ hydra:
   sweeper:
     params:
       # Sweep over FV grid sizes
-      N: 32
+      N: 64
       Re: 100

conf/experiment/validation/ghia/spectral.yaml

@@ -17,4 +17,4 @@ hydra:
       # Sweep over spectral solver types
       solver: spectral/fsg #,spectral/fsg
       Re: 100
-      N: 27
+      N: 12, 14, 16, 18, 20

conf/solver/fv.yaml

@@ -20,3 +20,8 @@ limiter: MUSCL
 alpha_uv: 0.4        # velocity under-relaxation
 alpha_p: 0.2         # pressure under-relaxation
 linear_solver_tol: 1.0e-9
+
+# Corner singularity treatment
+# Options: "none", "smoothing", or "saad"/"polynomial"
+corner_treatment: none
+corner_smoothing: 0.15   # smoothing width for "smoothing" method

conf/solver/spectral/sg.yaml

@@ -17,11 +17,11 @@ max_iterations: ${max_iterations}
 
 # Spectral-specific parameters
 basis_type: chebyshev    # "chebyshev" or "legendre"
-CFL: 0.5
+CFL: 2.5
 beta_squared: 5.0        # artificial compressibility parameter
 
 # Corner singularity treatment
-# Options: "smoothing" (simple cosine smoothing) or "subtraction" (Botella & Peyret 1998)
+# Options: "smoothing" or "saad"/"polynomial"
 corner_treatment: smoothing
 corner_smoothing: 0.15   # smoothing width (fraction of domain) for smoothing method
 

conf/validation/fv-regu.yaml

@@ -0,0 +1,3 @@
+# @package validation
+# Regularized FV reference data (Saad polynomial lid velocity)
+reference_dir: data/validation/fv-regu

conf/validation/fv.yaml

@@ -0,0 +1,3 @@
+# @package validation
+# Standard FV reference data (constant lid velocity)
+reference_dir: data/validation/fv

data/validation/fv-regu/Re1000/config.yaml

@@ -0,0 +1,32 @@
+Lx: 1.0
+Ly: 1.0
+N: 128
+Re: 1000
+experiment_name: LDC-Convergence
+lid_velocity: 1.0
+max_iterations: 100000
+mlflow:
+  mode: coolify
+  project_prefix: ''
+  tracking_uri: ${oc.env:MLFLOW_TRACKING_URI}
+plot_only: false
+solver:
+  Lx: ${Lx}
+  Ly: ${Ly}
+  Re: ${Re}
+  _target_: solvers.fv.solver.FVSolver
+  alpha_p: 0.2
+  alpha_uv: 0.4
+  convection_scheme: TVD
+  corner_smoothing: 0.15
+  corner_treatment: saad
+  lid_velocity: ${lid_velocity}
+  limiter: MUSCL
+  linear_solver_tol: 1.0e-09
+  max_iterations: ${max_iterations}
+  name: fv
+  nx: ${N}
+  ny: ${N}
+  tolerance: ${tolerance}
+sweep_name: regu-Re1000
+tolerance: 1.0e-06

data/validation/fv-regu/Re400/config.yaml

@@ -0,0 +1,32 @@
+Lx: 1.0
+Ly: 1.0
+N: 128
+Re: 400
+experiment_name: LDC-Convergence
+lid_velocity: 1.0
+max_iterations: 100000
+mlflow:
+  mode: coolify
+  project_prefix: ''
+  tracking_uri: ${oc.env:MLFLOW_TRACKING_URI}
+plot_only: false
+solver:
+  Lx: ${Lx}
+  Ly: ${Ly}
+  Re: ${Re}
+  _target_: solvers.fv.solver.FVSolver
+  alpha_p: 0.2
+  alpha_uv: 0.4
+  convection_scheme: TVD
+  corner_smoothing: 0.15
+  corner_treatment: saad
+  lid_velocity: ${lid_velocity}
+  limiter: MUSCL
+  linear_solver_tol: 1.0e-09
+  max_iterations: ${max_iterations}
+  name: fv
+  nx: ${N}
+  ny: ${N}
+  tolerance: ${tolerance}
+sweep_name: regu-Re400
+tolerance: 1.0e-06

data/validation/fv/Re100/config.yaml

@@ -0,0 +1,30 @@
+Lx: 1.0
+Ly: 1.0
+N: 128
+Re: 100
+experiment_name: LDC-Validation
+lid_velocity: 1.0
+max_iterations: 100000
+mlflow:
+  mode: coolify
+  project_prefix: ''
+  tracking_uri: ${oc.env:MLFLOW_TRACKING_URI}
+plot_only: false
+solver:
+  Lx: ${Lx}
+  Ly: ${Ly}
+  Re: ${Re}
+  _target_: solvers.fv.solver.FVSolver
+  alpha_p: 0.2
+  alpha_uv: 0.4
+  convection_scheme: TVD
+  lid_velocity: ${lid_velocity}
+  limiter: MUSCL
+  linear_solver_tol: 1.0e-09
+  max_iterations: ${max_iterations}
+  name: fv
+  nx: ${N}
+  ny: ${N}
+  tolerance: ${tolerance}
+sweep_name: Hpc-baseline-fv
+tolerance: 1.0e-06

data/validation/fv/Re1000/config.yaml

@@ -0,0 +1,30 @@
+Lx: 1.0
+Ly: 1.0
+N: 128
+Re: 1000
+experiment_name: LDC-Validation
+lid_velocity: 1.0
+max_iterations: 100000
+mlflow:
+  mode: coolify
+  project_prefix: ''
+  tracking_uri: ${oc.env:MLFLOW_TRACKING_URI}
+plot_only: false
+solver:
+  Lx: ${Lx}
+  Ly: ${Ly}
+  Re: ${Re}
+  _target_: solvers.fv.solver.FVSolver
+  alpha_p: 0.2
+  alpha_uv: 0.4
+  convection_scheme: TVD
+  lid_velocity: ${lid_velocity}
+  limiter: MUSCL
+  linear_solver_tol: 1.0e-09
+  max_iterations: ${max_iterations}
+  name: fv
+  nx: ${N}
+  ny: ${N}
+  tolerance: ${tolerance}
+sweep_name: Hpc-baseline-fv
+tolerance: 1.0e-06

data/validation/fv/Re400/config.yaml

@@ -0,0 +1,30 @@
+Lx: 1.0
+Ly: 1.0
+N: 128
+Re: 400
+experiment_name: LDC-Validation
+lid_velocity: 1.0
+max_iterations: 100000
+mlflow:
+  mode: coolify
+  project_prefix: ''
+  tracking_uri: ${oc.env:MLFLOW_TRACKING_URI}
+plot_only: false
+solver:
+  Lx: ${Lx}
+  Ly: ${Ly}
+  Re: ${Re}
+  _target_: solvers.fv.solver.FVSolver
+  alpha_p: 0.2
+  alpha_uv: 0.4
+  convection_scheme: TVD
+  lid_velocity: ${lid_velocity}
+  limiter: MUSCL
+  linear_solver_tol: 1.0e-09
+  max_iterations: ${max_iterations}
+  name: fv
+  nx: ${N}
+  ny: ${N}
+  tolerance: ${tolerance}
+sweep_name: Hpc-baseline-fv
+tolerance: 1.0e-06

main.py

@@ -94,6 +94,12 @@ def run_solver(cfg: DictConfig) -> str:
         log.info(f"Solving: {solver_name} N={cfg.N} Re={cfg.Re}")
         solver.solve()
 
+        # Compute validation errors against reference FV solution
+        reference_dir = cfg.get("validation", {}).get("reference_dir", "data/validation/fv")
+        validation_errors = solver.compute_validation_errors(reference_dir=reference_dir)
+        if validation_errors:
+            mlflow.log_metrics(validation_errors)
+
         mlflow.log_metrics(solver.metrics.to_mlflow())
         if solver.time_series:
             batch = solver.time_series.to_mlflow_batch()

scripts/hpc_submit.py

@@ -118,7 +118,7 @@ def main():
     parser = argparse.ArgumentParser(description="Submit HPC job array")
     parser.add_argument("experiment", help="Experiment (e.g., +experiment/validation/ghia=fv)")
     parser.add_argument("--queue", "-q", default="hpc", help="LSF queue (default: hpc)")
-    parser.add_argument("--time", "-W", default="1:00", help="Wall time (default: 1:00)")
+    parser.add_argument("--time", "-W", default="6:00", help="Wall time (default: 1:00)")
     parser.add_argument("--cores", "-n", type=int, default=4, help="Cores per job (default: 4)")
     parser.add_argument("--mem", default="6GB", help="Memory per core (default: 4GB)")
     parser.add_argument("--dry-run", action="store_true", help="Show commands without submitting")