Pardeep Kumar — Research notesNotes on numerical methods, scientific computing, and research software.https://kumarpardeep.com/enFrom Einstein’s equations to BSSN and FO-CCZ4https://kumarpardeep.com/blog/einstein-equations-bssn-fo-ccz4/https://kumarpardeep.com/blog/einstein-equations-bssn-fo-ccz4/Why the covariant field equations are not yet a time-marching algorithm, and how ADM, BSSN, CCZ4, and FO-CCZ4 reorganize spacetime geometry into numerical evolution systems.Sat, 18 Jul 2026 10:00:00 GMTnumerical relativityEinstein equationsBSSNCCZ4hyperbolic systemsA unified model for two-phase transport of CO₂-rich mixtureshttps://kumarpardeep.com/blog/multicomponent-co2-pipeline-transport/https://kumarpardeep.com/blog/multicomponent-co2-pipeline-transport/How HEM, a Helmholtz-energy EOS, stability analysis, a reformulated UVN flash, and equilibrium sound speed combine in multicomponent pipeline simulations.Sat, 18 Jul 2026 09:00:00 GMTmulticomponent flowCO₂ pipelinesUVN flashRiemann solversspeed of soundSolving the multicomponent UVN flash in TVN spacehttps://kumarpardeep.com/blog/uvn-flash-in-tvn-space/https://kumarpardeep.com/blog/uvn-flash-in-tvn-space/A step-by-step account of stability analysis, entropy maximization, the λ = −1/T result, the Helmholtz Q-function, and why eliminating nested temperature solves matters.Sat, 18 Jul 2026 08:00:00 GMTUVN flashphase stabilitythermodynamic optimizationHelmholtz energyFrom four equilibrium equations to one: faster pure-CO₂ depressurizationhttps://kumarpardeep.com/blog/reduced-vle-pure-co2/https://kumarpardeep.com/blog/reduced-vle-pure-co2/How the saturation curve reduces the pure-component UV flash, how differentiating the constraint yields a temperature ODE, and where the efficiency–conservation trade-off appears.Sat, 18 Jul 2026 07:00:00 GMTphase equilibriumCO₂ depressurizationdifferential-algebraic equationsfinite volume methodsWhy CO₂ pipeline transport is a thermodynamics problemhttps://kumarpardeep.com/blog/co2-pipeline-transport-foundations/https://kumarpardeep.com/blog/co2-pipeline-transport-foundations/From CCS infrastructure and phase envelopes to Riemann waves, water hammer, and a proposed CO₂-hammer benchmark: an accessible map of the modelling problem.Sat, 18 Jul 2026 06:00:00 GMTcarbon capture and storageCO₂ transportmultiphase flowthermodynamicsnumerical methods