[fruitful_ibox_row]
[fruitful_ibox column=”ffs-three-one” title=”Advection-Diffusion” link=”http://palha.org/research/mimetic/advection-diffusion” image=”http://palha.org/wp-content/uploads/2016/04/advection_diffusion_600x300.png”] Conservative advection-diffusion on arbitrary grids. details[/fruitful_ibox]
[fruitful_ibox column=”ffs-three-one” title=”Navier-Stokes flow 2D” link=”http://palha.org/research/mimetic/ns-flow” image=”http://palha.org/wp-content/uploads/2016/04/ns_flow_600x300.png” last=”true”] Mass, energy, enstrophy and vorticity (MEEV) conserving discretization for 2D Navier-Stokes flow problems. details[/fruitful_ibox]
[fruitful_ibox column=”ffs-three-one” title=”Navier-Stokes flow 3D” image=”http://palha.org/wp-content/uploads/2021/04/navier_stokes_3d_600x300.png” last=”true”] Dual-field mass, energy, and helicity conserving discretization for 3D Navier-Stokes flow problems. upcoming[/fruitful_ibox]
[fruitful_ibox column=”ffs-three-one” title=”Shallow waters” link=”http://palha.org/research/geophysical-fluids/shallow-waters” image=”http://palha.org/wp-content/uploads/2021/04/geophysical_flows_600x300.png”] Atmospheric shallow water flow on a flat plane and on the cubed sphere. details[/fruitful_ibox]
[fruitful_ibox column=”ffs-three-one” title=”Compressible Euler flow” link=”http://palha.org/research/geophysical-fluids/compressible-3d-euler” image=”http://palha.org/wp-content/uploads/2021/04/compressible_euler_600x300.png” last=”true”] Compressible 3D Euler flow on the cubed sphere. details[/fruitful_ibox][fruitful_ibox column=”ffs-three-one” title=”IMEX time integration” link=”http://palha.org/research/geophysical-fluids/imex-time-integration” image=”http://palha.org/wp-content/uploads/2021/04/imex_600x300.png” last=”true”] Exact spatial and temporal balance of energy exchanges within a horizontally explicit/vertically implicit non-hydrostatic atmosphere. details[/fruitful_ibox]
[fruitful_ibox column=”ffs-three-one” title=”Turbidity currents” link=”http://palha.org/research/geophysical-fluids/turbidity-currents” image=”http://palha.org/wp-content/uploads/2021/04/turbidity_currents_600x300.png” last=”true”] Conservative, physically compaticle dual-field discretization of turbidity currents. details[/fruitful_ibox]
[fruitful_ibox column=”ffs-three-one” title=”Laplace-Beltrami” last=”true” image=”http://palha.org/wp-content/uploads/2015/02/torus_eigenvalue_8_600x300.png”] Solution of the Laplace-Beltrami problem on 2D Riemannian manifolds embedded in $latex \mathbb{R}^{3}$.[/fruitful_ibox]
[fruitful_ibox column=”ffs-three-one” title=”Maxwell Eigenvalues” image=”http://palha.org/wp-content/uploads/2015/02/maxwell_eigenvalue_L_shaped_domain_600x300.png” last=”true”] Computation of the eigenvalues and eigenfunctions for the Maxwell ressonating cavity on a square with curved elements and on an L-shaped domain.[/fruitful_ibox]
[fruitful_ibox column=”ffs-three-one” title=”Mimetic Grad-Shafranov” link=”http://palha.org/research/mimetic/mimetic-grad-shafranov” image=”http://palha.org/wp-content/uploads/2015/06/mimetic_gs_psi_600x300.png” last=”true”] Solving the Grad-Shafranov equation on highly curved meshes conserving total plasma current. details[/fruitful_ibox]
[fruitful_ibox column=”ffs-three-one” title=”Darcy Flow” image=”http://palha.org/wp-content/uploads/2016/04/darcy_flow_slide_01_600x300.png”] Computation of Darcy flow with arbitrary permeability tensor, $latex \mathsf{K}$, and especially highly anisotropic permeability tensor.[/fruitful_ibox]
[fruitful_ibox column=”ffs-three-one” title=”2D Poisson” image=”http://palha.org/wp-content/uploads/2015/02/mimetic_poisson_square_crazy_mesh_02_shaped_600x300.png”] Solution of the 2D Poisson equation on highly curved meshes. [/fruitful_ibox]
[/fruitful_ibox_row]