Error Indicator based on the Multidimensional Positive Definite Advection Transport Algorithm...
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Transcript of Error Indicator based on the Multidimensional Positive Definite Advection Transport Algorithm...
Error Indicator based on the Multidimensional
Positive Definite Advection Transport Algorithm (MPDATA)
Joanna Szmelter Piotr K. Smolarkiewicz
Cranfield University NCAR
Royal Military College of Science Boulder
Shrivenham Colorado
Cartesian mesh MPDATA
Cartesian mesh MPDATA
MPDATA BASIC SCHEME
MPDATA BASIC SCHEME
MPDATA BASIC SCHEME
EDGE BASED FORMULATION
CONVERGENCE OF FINITE-VOLUME MPDATA ON UNSTRUCTURED MESH
CONVERGENCE OF FINITE-VOLUME MPDATA ON UNSTRUCTURED SKEWED MESH
ROTATING CYLINDER
BASIC MPDATA MPDATA+FTC
FCT
REVOLUTION OF A SPHERE AROUND THE DIAGONAL OF A DOMAIN
INITIAL MPDATA GAGE AFTER 1 REVOLUTION
INITIAL MPDATA GAGE
UPWIND LEAPFROG
EULER EQUATIONS – CONSERVATIVE FORM
NONOSCILLATORY FORWARD IN TIME FLOW SOLVERS
FLOW SOLVER
CONVERGENCE STUDY
MPDATA - NFT EULER SOLVER
M=0.5
MPDATA UPWIND
NACA 0012 COMPUTATIONAL MESH
AGARD MPDATA + FCT
M = 0.8 α = 1.25
MPDATA v AGARD SOLUTION
THE SAME MESH
MPDATA v R-K SOLUTION
EFFECT OF FCT
EFFECT OF PRESSURE SWITCH
ADAPTIVITY
REFINEMENT INDICATORS MESHING TECHNIQUES
REFINEMENT INDICATORS
From gradient of dependent variable Based on MPDATA lead error In the spirit of Richardson extrapolation Driven by an objective functional
LEAD ERROR
MPDATA ERROR INDICATOR
Remeshing Mesh movement Mesh enrichment P-refinement Combinations
MESHING TECHNIQUES
M = 2.5 α = 0
M = 2.5
Cp theoretical = 0.329
Cp computed <0.3334,0.3339>
M = 5
M = 15
Comparison of theoretical and computed shock angles for 15deg wedge
NACA64A010 OSCILLATING
AEROFOIL
M=0.796 k=0.2002
αm =1.01deg c=0.5m
Mesh movement
RAE 2822 M = 0.75 α = 3
RAE 2822 M = 0.75 α = 3
MPDATA 7523 pointsAGARD 20580 points
MPDATA fine mesh 16101 points
enrichment 11915 points
M = 0.8 α = 1.25
Pressure Contours
CONCLUSIONS
MPDATA evinces properties useful for construction of refinement indicators.
Edge-based data structure enables the use of MPDATA in conjunction with all standard adaptive meshing techniques known for unstructured meshes.
NFT MPDATA edge-based Euler solver has low implicit diffusion and remains accurate for a broad range of flow speeds.
Present work extends utility of MPDATA to new applications