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# 1D Multi-Component Inert Shock Tube | ||
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References: | ||
Reference: | ||
> P. J. Martínez Ferrer, R. Buttay, G. Lehnasch, and A. Mura, “A detailed verification procedure for compressible reactive multicomponent Navier–Stokes solvers”, Comput. & Fluids, vol. 89, pp. 88–110, Jan. 2014. Accessed: Oct. 13, 2024. [Online]. Available: https://doi.org/10.1016/j.compfluid.2013.10.014 | ||
## Initial Condition | ||
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![Initial Condition](initial.png) | ||
<img src="initial.png" height="MAX_HEIGHT"/> | ||
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## Results | ||
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![Results](result.png) | ||
<img src="result.png" height="MAX_HEIGHT"/> |
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# Lax shock tube problem (1D) | ||
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Reference: P. D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation, Communications on pure and applied mathematics 7 (1) (1954) 159–193. | ||
Reference: | ||
> P. D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation, Communications on pure and applied mathematics 7 (1) (1954) 159–193. | ||
## Initial Condition | ||
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![Initial Condition](initial.png) | ||
<img src="initial.png" height="MAX_HEIGHT"/> | ||
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## Result | ||
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![Result](result.png) | ||
<img src="result.png" height="MAX_HEIGHT"/> |
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# Shu-Osher problem (1D) | ||
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Reference: C. W. Shu, S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, Journal of Computational Physics 77 (2) (1988) 439–471. doi:10.1016/0021-9991(88)90177-5. | ||
Reference: | ||
> C. W. Shu, S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, Journal of Computational Physics 77 (2) (1988) 439–471. doi:10.1016/0021-9991(88)90177-5. | ||
## Initial Condition | ||
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![Initial Condition](initial.png) | ||
<img src="initial.png" height="MAX_HEIGHT"/> | ||
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## Result | ||
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![Result](result.png) | ||
<img src="result.png" height="MAX_HEIGHT"/> |
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# Titarev-Toro problem (1D) | ||
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Reference: V. A. Titarev, E. F. Toro, Finite-volume WENO schemes for three-dimensional conservation laws, Journal of Computational Physics 201 (1) (2004) 238–260. | ||
Reference: | ||
> V. A. Titarev, E. F. Toro, Finite-volume WENO schemes for three-dimensional conservation laws, Journal of Computational Physics 201 (1) (2004) 238–260. | ||
## Initial Condition | ||
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![Initial Condition](initial.png) | ||
<img src="initial.png" heiht="MAX_HEIGHT"/> | ||
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## Result | ||
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![Result](result.png) | ||
<img src="result.png" heiht="MAX_HEIGHT"/> |
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# 2D Hardcodied IC Example | ||
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## Initial Condition | ||
## Initial Condition and Result | ||
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![Initial Condition](initial.png) | ||
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## Result | ||
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![Result](result.png) | ||
<img src="initial.png" width="45%"/> | ||
<img src="result.png" width="45%"/> |
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## Result | ||
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![Result](result.png) | ||
<img src="result.png" height="MAX_HEIGHT"/> |
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# Isentropic vortex problem (2D) | ||
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Reference: Coralic, V., & Colonius, T. (2014). Finite-volume Weno scheme for viscous compressible multicomponent flows. Journal of Computational Physics, 274, 95–121. https://doi.org/10.1016/j.jcp.2014.06.003 | ||
Reference: | ||
> Coralic, V., & Colonius, T. (2014). Finite-volume Weno scheme for viscous compressible multicomponent flows. Journal of Computational Physics, 274, 95–121. https://doi.org/10.1016/j.jcp.2014.06.003 | ||
## Density | ||
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![Density](alpha_rho1.png) | ||
<img src="alpha_rho1.png" height="MAX_HEIGHT"/> | ||
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## Density Norms | ||
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![Density Norms](density_norms.png) | ||
<img src="density_norms.png" height="MAX_HEIGHT"/> |
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# Lid-Driven Cavity Problem (2D) | ||
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Reference: Bezgin, D. A., & Buhendwa A. B., & Adams N. A. (2022). JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows. arXiv:2203.13760 | ||
Reference: | ||
> Bezgin, D. A., & Buhendwa A. B., & Adams N. A. (2022). JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows. arXiv:2203.13760 | ||
Reference: Ghia, U., & Ghia, K. N., & Shin, C. T. (1982). High-re solutions for incompressible flow | ||
> Ghia, U., & Ghia, K. N., & Shin, C. T. (1982). High-re solutions for incompressible flow | ||
using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics, 48, 387-411 | ||
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Video: https://youtube.com/shorts/JEP28scZrBM?feature=share | ||
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## Final Condition | ||
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![Final Condition](final_condition.png) | ||
<img src="final_condition.png" height="MAX_HEIGHT"/> | ||
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## Centerline Velocities | ||
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![Centerline Velocities](centerline_velocities.png) | ||
<img src="centerline_velocities.png" height="MAX_HEIGHT"/> |
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# Rayleigh-Taylor Instability (2D) | ||
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## Final Condition | ||
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![Final Condition](final_condition.png) | ||
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## Centerline Velocities | ||
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![Linear Theory Comparison](linear_theory.jpg) | ||
## Final Condition and Linear Theory | ||
<img src='final_condition.png' height='MAX_HEIGHT'/> | ||
<img src='linear_theory.png' height='MAX_HEIGHT'/> |
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# 2D Riemann Test (2D) | ||
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Reference: Chamarthi, A., & Hoffmann, N., & Nishikawa, H., & Frankel S. (2023). Implicit gradients based conservative numerical scheme for compressible flows. arXiv:2110.05461 | ||
Reference: | ||
> Chamarthi, A., & Hoffmann, N., & Nishikawa, H., & Frankel S. (2023). Implicit gradients based conservative numerical scheme for compressible flows. arXiv:2110.05461 | ||
## Density Initial Condition | ||
## Density Initial and Final Conditions | ||
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![Density](alpha_rho1_initial.png) | ||
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## Density Final Condition | ||
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![Density Norms](alpha_rho1_final.png) | ||
<img src="alpha_rho1_initial.png" width="45%"/> | ||
<img src="alpha_rho1_final.png" width="45%"/> |
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# Shock Droplet (2D) | ||
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Reference: Panchal et. al., A Seven-Equation Diffused Interface Method for Resolved Multiphase Flows, JCP, 475 (2023) | ||
Reference: | ||
> Panchal et. al., A Seven-Equation Diffused Interface Method for Resolved Multiphase Flows, JCP, 475 (2023) | ||
## Initial Condition | ||
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![Initial Condition](initial.png) | ||
<img src="initial.png" height="MAX_HEIGHT"/> | ||
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## Result | ||
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![Result](result.png) | ||
<img src="result.png" height="MAX_HEIGHT"/> |
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# 2D Triple Point (2D) | ||
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Reference: | ||
> Trojak, W., & Dzanic, T. Positivity-preserving discoutinous spectral element method for compressible multi-species flows. arXiv:2308.02426 | ||
## Numerical Schlieren at Final Time | ||
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<img src="final.png" height="MAX_HEIGHT"/> | ||
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#!/usr/bin/env python3 | ||
import math | ||
import json | ||
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eps = 1e-8 | ||
Nx = 699 | ||
Ny = 299 | ||
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print(json.dumps({ | ||
# Logistics ================================================ | ||
'run_time_info' : 'F', | ||
# ========================================================== | ||
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# Computational Domain Parameters ========================== | ||
'x_domain%beg' : 0, | ||
'x_domain%end' : 7, | ||
'y_domain%beg' : 0, | ||
'y_domain%end' : 3, | ||
'm' : int(Nx), | ||
'n' : int(Ny), | ||
'p' : 0, | ||
'cfl_adap_dt' : 'T', | ||
'cfl_target' : 0.8, | ||
'n_start' : 0, | ||
't_stop' : 4.0, | ||
't_save' : 0.04, | ||
# ========================================================== | ||
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# Simulation Algorithm Parameters ========================== | ||
'num_patches' : 3, | ||
'model_eqns' : 2, | ||
'alt_soundspeed' : 'F', | ||
'num_fluids' : 2, | ||
'mpp_lim' : 'T', | ||
'mixture_err' : 'T', | ||
'time_stepper' : 3, | ||
'weno_order' : 7, | ||
'weno_eps' : 1.E-16, | ||
'weno_Re_flux' : 'F', | ||
'weno_avg' : 'F', | ||
'mapped_weno' : 'T', | ||
'null_weights' : 'F', | ||
'mp_weno' : 'F', | ||
'riemann_solver' : 2, | ||
'wave_speeds' : 1, | ||
'avg_state' : 2, | ||
'bc_x%beg' : -3,#11, | ||
'bc_x%end' : -3,#12 | ||
'bc_y%beg' : -3, | ||
'bc_y%end' : -3, | ||
# ========================================================== | ||
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# Formatted Database Files Structure Parameters ============ | ||
'format' : 1, | ||
'precision' : 2, | ||
'prim_vars_wrt' :'T', | ||
'schlieren_wrt' :'T', | ||
'fd_order' : 4, | ||
'schlieren_alpha(1)' : 0.5, | ||
'schlieren_alpha(2)' : 0.5, | ||
'parallel_io' :'T', | ||
# ========================================================== | ||
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# Patch 1: Left state ==================================== | ||
'patch_icpp(1)%geometry' : 3, | ||
'patch_icpp(1)%x_centroid' : 0.5, | ||
'patch_icpp(1)%y_centroid' : 3, | ||
'patch_icpp(1)%length_x' : 1, | ||
'patch_icpp(1)%length_y' : 6, | ||
'patch_icpp(1)%vel(1)' : 0., | ||
'patch_icpp(1)%vel(2)' : 0., | ||
'patch_icpp(1)%pres' : 1., | ||
'patch_icpp(1)%alpha_rho(1)' : (1 - eps)*1., | ||
'patch_icpp(1)%alpha_rho(2)' : eps, | ||
'patch_icpp(1)%alpha(1)' : 1 - eps, | ||
'patch_icpp(1)%alpha(2)' : eps, | ||
# ========================================================== | ||
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# Patch 2: Top right state ================================ | ||
'patch_icpp(2)%geometry' : 3, | ||
'patch_icpp(2)%alter_patch(1)' : 'T', | ||
'patch_icpp(2)%x_centroid' : 4, | ||
'patch_icpp(2)%y_centroid' : 2.25, | ||
'patch_icpp(2)%length_x' : 6, | ||
'patch_icpp(2)%length_y' : 1.5, | ||
'patch_icpp(2)%vel(1)' : 0., | ||
'patch_icpp(2)%vel(2)' : 0., | ||
'patch_icpp(2)%pres' : 0.1, | ||
'patch_icpp(2)%alpha_rho(1)' : (1-eps)*0.125, | ||
'patch_icpp(2)%alpha_rho(2)' : eps, | ||
'patch_icpp(2)%alpha(1)' : 1 - eps, | ||
'patch_icpp(2)%alpha(2)' : eps, | ||
# ========================================================== | ||
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# Patch 3: Bottom right state ============================= | ||
'patch_icpp(3)%geometry' : 3, | ||
'patch_icpp(3)%alter_patch(1)' : 'T', | ||
'patch_icpp(3)%x_centroid' : 4, | ||
'patch_icpp(3)%y_centroid' : 0.75, | ||
'patch_icpp(3)%length_x' : 6, | ||
'patch_icpp(3)%length_y' : 1.5, | ||
'patch_icpp(3)%vel(1)' : 0., | ||
'patch_icpp(3)%vel(2)' : 0., | ||
'patch_icpp(3)%pres' : 0.1, | ||
'patch_icpp(3)%alpha_rho(1)' : eps, | ||
'patch_icpp(3)%alpha_rho(2)' : (1 - eps)*1., | ||
'patch_icpp(3)%alpha(1)' : eps,# 0.95 | ||
'patch_icpp(3)%alpha(2)' : 1 - eps,#0.05, | ||
# ========================================================== | ||
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# Fluids Physical Parameters =============================== | ||
'fluid_pp(1)%gamma' : 1./(1.5 - 1.), | ||
'fluid_pp(1)%pi_inf' : 0, | ||
'fluid_pp(2)%gamma' : 1./(1.4 - 1.), | ||
'fluid_pp(2)%pi_inf' : 0., | ||
# ========================================================== | ||
})) |
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# Taylor-Green Vortex (3D) | ||
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Reference: Hillewaert, K. (2013). TestCase C3.5 - DNS of the transition of the Taylor-Green vortex, Re=1600 - Introduction and result summary. 2nd International Workshop on high-order methods for CFD. | ||
Reference: | ||
> Hillewaert, K. (2013). TestCase C3.5 - DNS of the transition of the Taylor-Green vortex, Re=1600 - Introduction and result summary. 2nd International Workshop on high-order methods for CFD. | ||
## Final Condition | ||
This figure shows the isosurface with zero q-criterion. | ||
![Density](result.png) | ||
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<img src="result.png" height="MAX_HEIGHT"/> | ||
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## Final Condition | ||
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![Density](result.png) | ||
<img src="result.png" height="MAX_HEIGHT"> | ||
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# Rayleigh-Taylor Instability (3D) | ||
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## Final Condition | ||
## Final Condition and Linear Theory | ||
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![Final Condition](final_condition.png) | ||
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## Centerline Velocities | ||
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![Linear Theory Comparison](linear_theory.png) | ||
<img src="final_condition.png" height="MAX_HEIGHT"/> | ||
<img src="linear_theory.png" height="MAX_HEIGHT"/> |
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