Field notes from a compressible multiphase CFD researcher — equations, code, interactive visualizations https://cfdblog.cc/en en-US noreply@cfdblog.cc (Younglin) Sun, 03 May 2026 20:09:47 GMT 1440 https://cfdblog.cc/en/posts/2026-05-04-implicit-diffusion-thomas-algorithm https://cfdblog.cc/en/posts/2026-05-04-implicit-diffusion-thomas-algorithm Mon, 04 May 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) 수치해석 implicit diffusion Thomas-algorithm stability https://cfdblog.cc/en/posts/2026-05-03-orlando-bonaventura-ap-imex-nonideal-gas https://cfdblog.cc/en/posts/2026-05-03-orlando-bonaventura-ap-imex-nonideal-gas Sun, 03 May 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) 논문리뷰 asymptotic-preserving IMEX low-mach Discontinuous-Galerkin non-ideal-gas https://cfdblog.cc/en/posts/2026-05-02-muscl-thinc-bvd-interface-reconstruction https://cfdblog.cc/en/posts/2026-05-02-muscl-thinc-bvd-interface-reconstruction Sat, 02 May 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) 논문리뷰 compressible-multiphase MUSCL THINC BVD interface-capturing https://cfdblog.cc/en/posts/2026-05-01-burgers-characteristics-shock-formation https://cfdblog.cc/en/posts/2026-05-01-burgers-characteristics-shock-formation Fri, 01 May 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) Burgers hyperbolic shock characteristics 수치해석 https://cfdblog.cc/en/posts/2026-04-30-cavitation-number-vapor-pressure https://cfdblog.cc/en/posts/2026-04-30-cavitation-number-vapor-pressure Thu, 30 Apr 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) 유체역학 Cavitation Multiphase Bernoulli 유동현상 https://cfdblog.cc/en/posts/2026-04-29-sph-meshfree-particle-hydrodynamics https://cfdblog.cc/en/posts/2026-04-29-sph-meshfree-particle-hydrodynamics Wed, 29 Apr 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) SPH Meshfree Lagrangian Multiphase Astrophysics https://cfdblog.cc/en/posts/2026-04-28-rankine-vortex-helmholtz https://cfdblog.cc/en/posts/2026-04-28-rankine-vortex-helmholtz Tue, 28 Apr 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) Vortex Vorticity 유체역학 유동현상 Helmholtz https://cfdblog.cc/en/posts/2026-04-27-amr-quadtree-cell-refinement https://cfdblog.cc/en/posts/2026-04-27-amr-quadtree-cell-refinement Mon, 27 Apr 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) AMR 쿼드트리 메시 알고리즘 수치해석 https://cfdblog.cc/en/posts/2026-04-26-casulli-walters-unstructured-shallow-water https://cfdblog.cc/en/posts/2026-04-26-casulli-walters-unstructured-shallow-water Sun, 26 Apr 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) 논문리뷰 shallow-water semi-implicit unstructured-grid https://cfdblog.cc/en/posts/2026-04-25-teno-low-dissipation-shock-capturing https://cfdblog.cc/en/posts/2026-04-25-teno-low-dissipation-shock-capturing Sat, 25 Apr 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) 논문리뷰 TENO WENO shock-capturing high-order https://cfdblog.cc/en/posts/2026-04-24-flux-limiter-tvd-advection https://cfdblog.cc/en/posts/2026-04-24-flux-limiter-tvd-advection Fri, 24 Apr 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) 알고리즘 TVD flux-limiter advection 수치해석 https://cfdblog.cc/en/posts/2026-04-23-plateau-rayleigh-jet-breakup https://cfdblog.cc/en/posts/2026-04-23-plateau-rayleigh-jet-breakup Thu, 23 Apr 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) Fluid Mechanics Flow Phenomena Plateau-Rayleigh Weber Number Ohnesorge Jet Breakup https://cfdblog.cc/en/posts/2026-04-22-cfd-linear-solvers-krylov https://cfdblog.cc/en/posts/2026-04-22-cfd-linear-solvers-krylov Wed, 22 Apr 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) Algorithms Linear-Solver Krylov Numerical Analysis https://cfdblog.cc/en/posts/2026-04-22-wall-distance-eikonal-fast-marching https://cfdblog.cc/en/posts/2026-04-22-wall-distance-eikonal-fast-marching Wed, 22 Apr 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) Algorithm Eikonal Fast-Marching Mesh https://cfdblog.cc/en/posts/2026-04-21-reynolds-number-scale-fluid-mechanics https://cfdblog.cc/en/posts/2026-04-21-reynolds-number-scale-fluid-mechanics Tue, 21 Apr 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) Fluid Mechanics Flow Phenomena Reynolds Non-dimensionalization https://cfdblog.cc/en/posts/2026-04-20-discontinuous-galerkin-method-cfd https://cfdblog.cc/en/posts/2026-04-20-discontinuous-galerkin-method-cfd Mon, 20 Apr 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) FEM DGM High-Order Accuracy Compressible Flow https://cfdblog.cc/en/posts/2026-04-20-fem-rigid-body-dynamics-quaternion https://cfdblog.cc/en/posts/2026-04-20-fem-rigid-body-dynamics-quaternion Mon, 20 Apr 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) FEM Rigid Body Dynamics Quaternion https://cfdblog.cc/en/posts/2026-03-28-dean-flow-analytical-solution https://cfdblog.cc/en/posts/2026-03-28-dean-flow-analytical-solution Sat, 28 Mar 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) Analytical Solution Classical Flow CFD Validation Dean Flow Secondary Flow Helical Pipe https://cfdblog.cc/en/posts/2026-03-28-poiseuille-flow-analytical-solution https://cfdblog.cc/en/posts/2026-03-28-poiseuille-flow-analytical-solution Sat, 28 Mar 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) Analytical Solution Classical Flow CFD Validation Poiseuille Finite Difference https://cfdblog.cc/en/posts/2026-03-27-simpleFoam-pressure-divergence https://cfdblog.cc/en/posts/2026-03-27-simpleFoam-pressure-divergence Fri, 27 Mar 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) CFD Practice QA OpenFOAM SIMPLE Convergence https://cfdblog.cc/en/posts/2026-03-26-openfoam-backward-facing-step https://cfdblog.cc/en/posts/2026-03-26-openfoam-backward-facing-step Thu, 26 Mar 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) OpenFOAM Tutorial simpleFoam BackwardFacingStep Turbulence 1000): vector directions become irregular and vortex st… --- Read more: https://cfdblog.cc/en/posts/2026-03-25-reynolds-flow-transition-visualization]]> https://cfdblog.cc/en/posts/2026-03-25-reynolds-flow-transition-visualization https://cfdblog.cc/en/posts/2026-03-25-reynolds-flow-transition-visualization Wed, 25 Mar 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) 시각화 Reynolds 유동천이 유체역학 https://cfdblog.cc/en/posts/2026-03-24-paper-review-pinn-turbulence-modeling https://cfdblog.cc/en/posts/2026-03-24-paper-review-pinn-turbulence-modeling Tue, 24 Mar 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) 논문리뷰 PINN 딥러닝 난류모델 https://cfdblog.cc/en/posts/mach-architect https://cfdblog.cc/en/posts/mach-architect Wed, 11 Mar 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) CFD Compressible-Flow Interactive Isentropic Nozzle https://cfdblog.cc/en/posts/rhie-chow-multiphase https://cfdblog.cc/en/posts/rhie-chow-multiphase Tue, 10 Mar 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) Multiphase Rhie-Chow OpenFOAM Numerical-Methods Approximate derivatives directly as differences. This is the most intuitive approach. It approximates derivatives by performing a Taylor expansion of the function values at grid points (nodes). Mathematical Origin: Taylor Expansion Taylor expansion at point [math]: [equation] From this, difference approximations are derived: Forward Difference: [equation] Central Difference: [equation] Second Derivative: [equation] Application to Advection-Diffusion Using central differences: [equation] This results in a system of coupled ODEs for the unknowns [math] at the grid points. Pros and Cons Pros: - Simple concept and easy implementation - Highly efficient on structured grids - Easy to achieve high-order accuracy (compact schemes, spectral-like schemes) - Clean matrix structure on orthogonal grids (band matrix) Cons: - Difficult to apply to unstructured grids - this is a critical limitation - Grid generation for complex ge… --- Read more: https://cfdblog.cc/en/posts/fdm-fem-fvm]]> https://cfdblog.cc/en/posts/fdm-fem-fvm https://cfdblog.cc/en/posts/fdm-fem-fvm Mon, 09 Mar 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) CFD FDM FEM FVM Numerical-Methods https://cfdblog.cc/en/posts/numerical-dungeon https://cfdblog.cc/en/posts/numerical-dungeon Sun, 08 Mar 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) CFD Numerical-Methods Interactive Education https://cfdblog.cc/en/posts/five-equation-model https://cfdblog.cc/en/posts/five-equation-model Sat, 07 Mar 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) Multiphase Diffuse-Interface Python Implementation https://cfdblog.cc/en/posts/interface-capturing https://cfdblog.cc/en/posts/interface-capturing Fri, 06 Mar 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) Multiphase VOF Level-Set Diffuse-Interface To find the flux at a cell boundary, treat the average values of the two adjacent cells as the left and right states and solve the Riemann problem. The update formula for the Finite Volume Method: [equation] where [math] is the numerical flux determined from the solution to the Riemann problem. Exact Riemann Solver An exact Riemann solver finds the pressure in the star region, [math], using the Newton-Raphson iterative method. Rankine-Hugoniot relations or isentropic relations are applied depending on the type of wave (shock or rarefaction). Shock wave relation ([math], [math] or [math]): [equation] where [math] and [math]. Rarefaction wave relation ([math]): [equation] … --- Read more: https://cfdblog.cc/en/posts/riemann-solvers]]> https://cfdblog.cc/en/posts/riemann-solvers https://cfdblog.cc/en/posts/riemann-solvers Thu, 05 Mar 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) Riemann-Solver Godunov Numerical-Methods "The history of compressible multiphase numerics is the history of fighting pressure oscillations." Plain conservative finite volume schemes produce spurious oscillations when [math] takes intermediate values … --- Read more: https://cfdblog.cc/en/posts/compressible-multiphase-intro]]> https://cfdblog.cc/en/posts/compressible-multiphase-intro https://cfdblog.cc/en/posts/compressible-multiphase-intro Wed, 04 Mar 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) CFD Multiphase Compressible-Flow Introduction https://cfdblog.cc/en/posts/draft-post https://cfdblog.cc/en/posts/draft-post Wed, 04 Mar 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) Draft Test https://cfdblog.cc/en/posts/hello-blog https://cfdblog.cc/en/posts/hello-blog Tue, 03 Mar 2026 00:00:00 GMT noreply@cfdblog.cc (Younglin) Next.js Contentlayer MDX LaTeX