The Mach Number Goes to Zero, the Time Step Doesn't Budge — Reproducing an IMEX TVD Scheme
A second-order IMEX scheme that escapes the acoustic CFL without oscillating
Un-smearing the Interface Every Step — Implementing Anti-Diffusion Sharpening (IST)
A post-processing technique that pins a numerically smeared interface to a constant thickness
Supersonic Flow Can't See Upstream — Characteristics and Sound Waves in the Euler Equations
Why a small disturbance splits into three characteristic speeds
Letting Sound and Matter Flow Separately — Acoustic-Convective Splitting (Lagrange-Projection)
Implementing the Lagrange-Projection scheme that sidesteps low-Mach stiffness by splitting acoustics from convection
[Paper Review] Tired of Differentiating Jacobians by Hand? — Operator-Overloading Automatic Differentiation (ADOO)
Fraysse (2019): getting the exact flux Jacobian for implicit CFD with zero hand differentiation
When Explicit Blows Up, Solve Implicit Without Inverting the Matrix — LU-SGS
Implicit time-stepping stability and the LU-SGS factorization, verified in code
Catching Shocks Without Multiplying a Matrix at Every Face — AUSM Flux Splitting
How AUSM splits the Euler flux to capture shocks without Roe — with code
[Paper Review] Drawing Shocks with tanh — Implementing TENO-THINC Reconstruction
How THINC keeps a sub-cell jump alive when polynomials smear the contact
Filling an Interface with a Fluid That Isn't There — The Ghost Fluid Method
GFM for sharp interfaces in compressible multi-material flow
The Euler Eigensystem in an Arbitrary Direction — Three Waves, Two Repeats, One Singularity
Where the left eigenvector breaks when n̂ tilts, and the three conventions that dodge it
How to Make an Outflow Stop Reflecting Sound — Navier–Stokes Characteristic Boundary Conditions
The single most common cause of compressible-solver blow-ups, tamed by one parameter σ
[Paper Review] One Scheme Can't Handle Every Wave — Chamarthi (2025)
Wave-appropriate reconstruction for compressible multicomponent flows — THINC at contacts, MP5 at shocks, central at viscous tangentials