When Explicit Blows Up, Solve Implicit Without Inverting the Matrix — LU-SGS
·5 min read
Implicit time-stepping stability and the LU-SGS factorization, verified in code
Catching Shocks Without Multiplying a Matrix at Every Face — AUSM Flux Splitting
·6 min read
How AUSM splits the Euler flux to capture shocks without Roe — with code
[Paper Review] Drawing Shocks with tanh — Implementing TENO-THINC Reconstruction
·6 min read
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
·6 min read
GFM for sharp interfaces in compressible multi-material flow
The Euler Eigensystem in an Arbitrary Direction — Three Waves, Two Repeats, One Singularity
·5 min read
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
·5 min read
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)
·7 min read
Wave-appropriate reconstruction for compressible multicomponent flows — THINC at contacts, MP5 at shocks, central at viscous tangentials