Research

SAGEST Predictive Simulation Center · CFD & Propulsion Laboratory, UVA

2025-2026

SAGEST (Stochastic Simulations of Ablative Geometries with Error-Learning in Space and Time) is a DOE/NNSA PSAAP IV predictive simulation center led from the University of Virginia, with hypersonic flight as its test case. I worked in Dr. Xinfeng Gao's CFD & Propulsion Laboratory on the meshing side of that problem.

The target is a Maneuverable Reentry Vehicle (MaRV) at 40 km and $M_{\infty} = 12.6$ , simulated in Chord, a fourth-order explicit finite-volume solver. Chord only accepts fully structured, pure-hexahedral multiblock meshes, and the vehicle's split flaps meet the cone in point-terminated corners that no hexahedral topology can fill.

2025-2026

Undergraduate Researcher · CFD & Propulsion Laboratory

Built fully structured, pure-hexahedral multiblock meshes of a Mach 12.6 biconic reentry vehicle in Fidelity Pointwise for a fourth-order finite-volume solver: 1:1 conformal faces, 8n edge sizing, no degenerate edges.
Removed a degenerate flap-hinge topology with a 0.01 in CAD trim, and bounded its cost at a 0.44% change in flap planform area.
Reached the M∞ = 12.6 design condition in ANSYS Fluent by sequential Mach ramping (density-based, Roe FDS / AUSM, Spalart–Allmaras).
Ran a ~78 M-cell refinement study showing that block-aligned field discontinuities survive refinement, so resolution alone is not their cause.
Built a ~1 M-cell prism–tetrahedral comparison mesh with y⁺ ≈ 1 inflation layers to isolate the effect of the geometry approximation.
Presented weekly to the lab in LaTeX/Beamer; co-authored the project's research poster.

Freestream: $M_{\infty} = 12.6$
Altitude: 40 km
Conditions: 277.52 Pa · 251.05 K
Geometry: 10.5° / 7° bicone, split flap
Mesher: Fidelity Pointwise
Solvers: Chord (target) · ANSYS Fluent

Interactive Vehicle Model

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Interactive Structured Mesh

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Hex cells: 119,296
Nodes: 131,490
Tets / prisms / pyramids: 0
Wall faces: 8,448
Mean wall skewness: 0.099
All faces: 370,048

Coarse mesh iteration 4 (August 2026), read straight from the Fluent case file Pointwise exported. Skewness here is the 2D equiangle skewness of each quad face, $max (\frac{θ _{m a x} - 9 0 ^{\circ}}{9 0 ^{\circ}}, \frac{9 0 ^{\circ} - θ _{m i n}}{9 0 ^{\circ}})$ , computed for this page.

Wall surface (8,448 faces)All mesh faces (370,048)

Face set	Mean	95th pct.	Max	> 0.85
Wall surface	0.099	0.468	0.9459	36
All mesh faces	0.098	0.438	0.9996	1,629

Most faces above 0.85 sit in the slice and flap region (x ≈ 25–32 in): at the slice leading edge and where the triangular wedge faces are split into quads.

June 2026

Structured Benchmark in ANSYS

The first structured mesh was built top-down in ANSYS: slice the domain into blocks, then sweep each one. A conical O-grid wrap at the nose, adapted from labmate Gabe Damiani's conic meshing approach, reduced skew in the front cells, and manual edge biasing carried resolution across the 10.5° to 7° cone junction. An earlier, coarser version ran and produced the right physics: an attached oblique shock, a hot shock layer, and a Mach 12.5 freestream, matching earlier tetrahedral results.

Full structured benchmark mesh — 100% hex benchmark mesh, xy centerplane; fine at the wall and cone, coarse toward the far field.

Conical O-grid nose — Nose O-grid with a conical wrap (adapted from G. Damiani's conic meshing); the square core absorbs the stagnation-point singularity.

Forced flap subdivision — Flap region: feature edges failed to project, forcing a manual decomposition. Still 100% hex, but skewed.

Nose O-grid front view — Front view: inner square core, petals and rings sweep cleanly; 100% hex maintained.

The workflow hit a wall the solver could not fix. The many geometry operations left tiny gaps between blocks, so interior block faces imported as one-sided walls that physically blocked the flow. Zone-type reassignment, interior naming, interface pairing, and SpaceClaim gap repair all failed, which moved the work to a dedicated structured mesher.

Mach contour on the benchmark mesh — Earlier mesh, Mach 0 to 15: oblique shock hugging the cone at M∞ = 12.5.

Slice-boundary wall artifact — Refined mesh: interior slice faces imported as walls, and the flow stops at block boundaries.

July 2026

Pointwise: Domain and Blocking

In Pointwise the mesh is built bottom-up from the surface. The outer boundary follows the shock envelope instead of a rectangular box, so cells are spent where the gradients are. Chord's 8n edge rule sets the coarsest legal block at 9 nodes (8 cells) per edge, and every subdivision propagates through the whole index space up- and downstream. That propagation constraint drove every decision after it.

Shock-fitted domain design sketch — Design sketch: a domain that follows the shock envelope instead of a rectangular far field.

First full Pointwise mesh — As built: first full-vehicle iteration.

Butterfly O-H nose grid — Butterfly O-H grid on the nose; the square core takes the stagnation singularity.

Flap junction blocking with quality coloring — Flap junction blocking: minimum included angles of 21° to 88.5°, worst on the decomposition edges.

First full-mesh iteration	Value	Note
Total cells	247,296	deliberately coarse
Blocks	64
Jacobian	$1.12 \times 1 0^{- 5} to 8.76 \times 1 0^{- 4}$	positive throughout: valid mapping
Min / max included angle	21.1° / 173.6°	ideal 90°; localized at the flap decomposition

July 2026

The Hinge Singularity

Where the two flap panels meet the shoulder, the geometry ends in a point. Any block that fills that corner needs a collapsed edge, so its Jacobian goes to zero, and Chord requires $J > 0$ everywhere. With two flaps, the far-field extrusion inherits both pinch points. The fix had to be geometric: trim $δ = 0.01$ in off each outboard flap edge in SolidWorks, which turns the point into a short, finite, meshable edge.

Flap hinge close-up — Hinge region: the point-terminated corner becomes a finite edge after the trim.

Flap trim schematic — Plan view: δ = 0.01 in removed from each outboard flap edge (exaggerated for clarity).

Surface	ΔA (in²)
Flap planform (2.29 → 2.28 in, ×2)	−0.066
Shoulders (2.77 × δ, ×2)	+0.055
Exposed base (0.53 × δ, ×2)	+0.011
Net	0.000

\frac{Δ A}{A _{flaps}} = \frac{0.066 in ^{2}}{15.11 in ^{2}} = 0.44%

Every square inch removed from the flaps reappears on the shoulders and base, and the wedge angle is unchanged. High- $C_{p}$ flap surface is traded for near-zero- $C_{p}$ shoulder and base, so the force change is bounded by 0.44%. The price is a thin sliver band along the trimmed edge, a large transverse spacing jump the blocking has to route around.

Unapproximated geometry, tetrahedral run — Original geometry on tets: AUSM diverged at ~4,400 iterations; finished on Roe FDS.

Approximated geometry, tetrahedral run — Trimmed geometry on tets: AUSM stable throughout.

Quick tetrahedral runs under the 1.048 M-cell student license cap, used to test the trim qualitatively. Neither converged at $M_{\infty} = 12.6$ ; the trimmed geometry behaved marginally better. The two runs differ in flux scheme, so they carry no quantitative weight.

July 2026

Pure-Hex Volume Blocking

With the hinge resolved, the surface mesh and the full volume blocking went through: every face quadrilateral, every edge finite, block boundaries following the cone junction, slice, and flap edges into the volume. The nose moved from an O-H grid to a simple extrusion, which meant fewer awkward subdivisions at the cost of skew in the nose region.

Shaded surface mesh — Structured surface mesh on the trimmed geometry.

Flap panel surface mesh — Flap panel: all quads, all finite edges.

Full vehicle blocking colored by Jacobian — Full-vehicle blocking, colored by Jacobian.

Flap region blocking colored by skewness — Flap region, equiangle skewness: the leading corner concentrates skew locally, with no collapsed edges.

Nose blocking — Nose: simple extrusion with a sliced cutplane.

Rear blocking — Rear: block boundaries follow the slice and flap edges into the volume.

Inviscid Mach contour on the structured mesh — Euler solution on the structured mesh, xy centerplane.

Inviscid residual history — 20,000 iterations at a flat CFL of 1: transients decay by ~11k iterations, then hold at 1e-2 to 1e-1.

August 2026

Mach Ramping to the Design Condition

Cold-started RANS converged cleanly at $M_{\infty} = 8$ and stalled above it. Warm-starting each Mach number from the last converged field got the solution to the design condition: every step recovered, with no divergence and no scheme intervention.

M 4→M 6→M 8→M 9.5→M 11→M 12.6

Ramp	Setting
Schedule	~5,000 iterations per condition, no re-initialization between steps
Flux	Roe FDS throughout; AUSM for the final ~5,000 iterations
Model	Density-based, ideal gas, Sutherland viscosity, Spalart–Allmaras, adiabatic no-slip walls
Residuals	Each step spikes 2–3 orders, then relaxes; floor rises from 1e-3–1e-4 to 1e-1–1e-2 at M 12.6

Residual history across the Mach ramp — Residual history: each spike is a far-field Mach increment. The turbulence (νₜ) residual holds at 1e-6 throughout.

Mach contour at M 12.6, centerplane — Design condition, xy centerplane: bow shock tight to the nose, thin shock layer, flap compression.

Mach contour at M 12.6, isometric — Design condition, isometric.

Mach contour at M 12.6, slice flap plane — Design condition, slice-flap plane.

A rising floor with a flat turbulence residual pointed at the mesh, not the model. Rebuilding the nose with an expanded hemisphere wrap pushed skew radially outward from the stagnation region and removed the radial artifacts at the tip; a seam remained at the nose-to-cone transition.

Equiangle skewness after the nose rework — After the nose rework: peak skew reduced and spread over a larger region.

Keyhole topology skewness — Keyhole cross-section: the upper half carries the flap subdivisions; peak skew sits where the cylindrical wrap meets the extrusion.

August 2026

Refinement Study: ~78 M Cells

The structured solutions showed sharp discontinuities aligned with interior block faces at three sites: the nose-to-cone junction, the flat-slice transition, and the base corner. The test was to hold geometry, topology, and solver settings fixed and change only the cell count. If the features were discretization error, they would fade under refinement.

Mach contour, ~78 M-cell refined mesh, M∞ = 6

Mach contour, coarse structured mesh, M∞ = 12.6

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Coarse · M 12.6~78 M cells · M 6

Drag the handle (or use ← →) to compare.

Mach number on the xy centerplane. The refined run reached M 6 in the available wall time, so the color scales differ (left: coarse, right: refined) and shock standoff changes with Mach. The comparison is structural: where the seams are, and whether they move.

Refined mesh, nose zoom — (a) Nose: cell-scale waviness along the bow shock near the stagnation line.

Refined mesh, flat slice zoom — (b) Flat slice: the expansion at the slice edge is physical; the straight seam downstream is not.

Refined mesh, base corner zoom — (c) Base corner: a faint vertical seam in the wake.

Region	Observation	Most consistent with
(a) Nose	Scalloped bow shock, amplitude ~1 cell; persists at shorter wavelength	Grid-induced: shock oblique to cell faces
(b) Flat slice	Mesh-aligned seam bounding the near-wall region	Mixed: physical expansion fan plus the high-aspect-ratio band from the trim
(c) Base corner	Vertical seam above the corner; isolated low-value cells	Grid-induced, plus possible non-convergence in the wake

Refinement bought a thinner shock layer, a boundary layer distinct from the shock, and a resolved base recirculation that the coarse mesh missed. None of the three seams disappeared, so resolution alone is not the cause: they are tied to the block topology, the physics, or both. A tetrahedral run of the untrimmed geometry (unconverged, used for structure only) shows the same global flow with no block-aligned seams, because it has no block faces.

Refined mesh, top-down Mach — Top-down Mach on the refined mesh: a step across the flap midline aligned with the block face between the two flap regions.

Refined mesh residual history — Refined-mesh residuals: streamwise momentum, energy, and continuity keep descending; y and z momentum plateau at 1e-2 to 1e-3.

Research Poster

Structured Hexahedral Mesh Generation for a Biconic Maneuverable Reentry Vehicle

Arda Alpan, Gabe Damiani, Stephen Guzik, Xinfeng Gao · UVA CFD & Propulsion Laboratory

Open the poster (PDF)