Reconstruction for 1D BlockFV by Sreeram-Shankar · Pull Request #3156 · trixi-framework/Trixi.jl

Sreeram-Shankar · 2026-07-26T18:21:03Z

Summary

Part of #3155 (Reconstructions for Block Finite Volume).

This PR adds second-order MUSCL-type reconstructions for the 1D TreeMesh BlockFV solver. The first-order BlockFV path is left unchanged. A new BlockFVO2 solver (with VolumeIntegralFiniteVolumeO2) is introduced for the O2 scheme.

Added BlockFVO2 / VolumeIntegralFiniteVolumeO2 with a reconstruction API (reconstruction_mode, slope_limiter, cons2recon / recon2cons).
Volume-local reconstruction at internal subcell faces
Surface reconstruction at element interfaces and boundaries via specialized prolong2interfaces! / prolong2boundaries!
BlockFV-specific reconstruction_O2 function
1D TreeMesh only for now
Examples and tests (elixir + convergence and L2/Ling tests) are included

github-actions · 2026-07-26T18:21:15Z

codecov · 2026-07-26T18:56:32Z

Codecov Report

❌ Patch coverage is 96.62921% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 96.95%. Comparing base (630c6ee) to head (959daf0).

Files with missing lines	Patch %	Lines
src/solvers/blockfv/blockfv_1d.jl	96.15%	3 Missing ⚠️

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jlchan

This is looking like a great draft. When you have time, could you share results from a convergence test and a comparison of solution profiles for BlockFV vs BlockFVO2?

Once you've had a chance to add CI tests and a NEWS.md entry, please feel free to ping me again

Sreeram-Shankar · 2026-07-26T23:37:32Z

l2
rho                         rho_v1                   rho_e_total         
error         EOC      error        EOC       error        EOC       
1.72e-04  -            1.77e-04  -            5.49e-04  -         
4.01e-05  2.10      4.19e-05  2.08      1.41e-04  1.96      
9.57e-06  2.07      1.03e-05  2.02      3.52e-05  2.00      

mean      2.08         mean      2.05          mean      1.98      

linf
rho                      rho_v1                 rho_e_total         
error        EOC      error         EOC      error        EOC       
6.23e-04  -          6.00e-04  -           1.36e-03  -         
1.57e-04  1.99      1.56e-04  1.95      3.46e-04  1.98      
4.19e-05  1.90      4.15e-05  1.90      8.94e-05  1.95      

mean      1.95           mean      1.93      mean      1.96

Convergence Test

Sreeram-Shankar · 2026-07-27T00:07:16Z

jlchan · 2026-07-27T00:21:18Z

Nice! Can you also show a comparison for a shock or discontinuous solution?

Sreeram-Shankar · 2026-07-27T00:59:02Z

jlchan

Thanks for making the changes before! One question

jlchan · 2026-08-05T03:06:24Z

The CI failure looks real, can you fix it? Prob just a namespace issue

ranocha

Thanks for working on this!

ranocha · 2026-08-05T07:54:47Z

+"""
+    BlockFVO2(; n_nodes::Integer,
+                surface_flux,
+                slope_limiter = minmod,
+                cons2recon = cons2prim,
+                recon2cons = prim2cons,
+                RealT = Float64)
+
+Create a second-order block finite volume solver with high-order volume reconstruction.
+See [`VolumeIntegralFiniteVolumeO2`](@ref).
+
+!!! warning "Experimental code"
+    This code is experimental and may change in any future release.
+"""
+const BlockFVO2 = DG{Basis, Mortar, SurfaceIntegral,


I don't think we need a new solver alias for this, do we? Can't we just continue to use BlockFV as before, maybe with a new method accepting a reconstruction?

ranocha · 2026-08-05T08:02:24Z

+        # Near the element ends the missing neighbor is clamped to the
+        # outermost cell (volume-local stencil; no values from other elements).


We have some options (the reconstruction_mode) for choosing how to handle cell boundaries for

Trixi.jl/src/solvers/dg.jl

Lines 598 to 660 in 0aaa001

"""

VolumeIntegralPureLGLFiniteVolumeO2(basis;

volume_flux_fv = flux_lax_friedrichs,

reconstruction_mode = reconstruction_O2_full,

slope_limiter = minmod,

cons2recon = cons2prim,

recon2cons = prim2cons)

This gives an up to second order accurate finite volume scheme on an LGL-type subcell

mesh (LGL = Legendre-Gauss-Lobatto).

Depending on the `reconstruction_mode` and `slope_limiter`, experimental orders of convergence

between 1 and 2 can be expected in practice.

Since this is a volume integral, all reconstructions are purely cell-local, i.e.,

no neighboring elements are queried at reconstruction stage.

The interface values of the inner DG-subcells are reconstructed using the standard MUSCL-type reconstruction.

For the DG-subcells at the boundaries, two options are available:

1) The unlimited slope is used on these cells.

This gives full second order accuracy, but also does not damp overshoots between cells.

The `reconstruction_mode` corresponding to this is `reconstruction_O2_full`.

2) On boundary subcells, the solution is represented using a constant value, thereby falling back to formally only first order.

The `reconstruction_mode` corresponding to this is `reconstruction_O2_inner`.

In the reference below, this is the recommended reconstruction mode and is thus used by default.

**Symmetric** total-Variation-Diminishing (TVD) choices for the `slope_limiter` are

1) [`minmod`](@ref)

2) [`monotonized_central`](@ref)

3) [`superbee`](@ref)

4) [`vanleer`](@ref)

5) [`koren_symmetric`](@ref)

**Asymmetric** TVD limiters are also available, e.g.,

1) [`koren`](@ref) for positive (right-going) velocities

2) [`koren_flipped`](@ref) for negative (left-going) velocities

The reconstruction is performed in reconstruction variables, which default to the primitive variables.

Other choices are possible, e.g., thermodynamic variables, see [`cons2thermo`](@ref) and [`thermo2cons`](@ref)

for [`NonIdealCompressibleEulerEquations1D`](@ref) and [`NonIdealCompressibleEulerEquations2D`](@ref).

!!! note "Conservative systems only"

Currently only implemented for systems in conservative form, i.e.,

`have_nonconservative_terms(equations) = False()`

## References

See especially Section 3.2, Section 4, and Appendix D of the paper

- Rueda-Ramírez, Hennemann, Hindenlang, Winters, & Gassner (2021).

"An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations.

Part II: Subcell finite volume shock capturing"

[JCP: 2021.110580](https://doi.org/10.1016/j.jcp.2021.110580)

"""

struct VolumeIntegralPureLGLFiniteVolumeO2{SubCellInterfaceCoordinates, VolumeFluxFV,

Reconstruction, Limiter,

Cons2Recon, Recon2Cons} <:

AbstractVolumeIntegralPureLGLFiniteVolume

sc_interface_coords::SubCellInterfaceCoordinates # (x-)coordinates of the sub-cell element interfaces

volume_flux_fv::VolumeFluxFV # non-symmetric in general, e.g. entropy-dissipative

reconstruction_mode::Reconstruction # which type of FV reconstruction to use

slope_limiter::Limiter # which type of slope limiter function

cons2recon::Cons2Recon # function to convert from conservative variables to the variables used for reconstruction

recon2cons::Recon2Cons # function to convert from the variables used for reconstruction back to conservative variables

end

Could we please enable the same flexibility here (and more options later)? We should also cross-reference these methods from their docstrings.

DanielDoehring · 2026-08-23T14:17:32Z

Could you also provide a figure how this looks for reconstruction_mode_inner ?

Sreeram-Shankar · 2026-08-25T16:38:26Z

Could you re-upload the image? Im not able to see it

DanielDoehring · 2026-08-26T10:02:50Z

Could you re-upload the image? Im not able to see it

Strange 🤔 , it is the one you posted here.

jlchan · 2026-08-26T12:40:46Z

Could you re-upload the image? Im not able to see it

Strange 🤔 , it is the one you posted here.

I actually can't view the image either @DanielDoehring. Can you specify which one it is?

DanielDoehring · 2026-08-26T12:43:29Z

This one

Reconstruction for 1D BlockFV

66550b2

fix typos sigh

dbd21b2

Sreeram-Shankar added 2 commits July 26, 2026 13:59

remove unwated reconstruction options

960e257

fix whitespace formatting

442ac74

jlchan reviewed Jul 26, 2026

View reviewed changes

Comment thread src/solvers/blockfv/blockfv.jl Outdated

Comment thread src/solvers/blockfv/blockfv_1d.jl

Comment thread src/solvers/blockfv/blockfv_1d.jl

Comment thread src/solvers/blockfv/blockfv_1d.jl

Sreeram-Shankar added 2 commits July 26, 2026 17:37

Add an example and test for fvO2

3ecbeb3

fix another typo

ca8d5a8

Sreeram-Shankar added 2 commits July 26, 2026 18:46

Add comments and diagrams

279b14e

news entry

fa144ba

Sreeram-Shankar requested a review from jlchan July 27, 2026 00:08

jlchan reviewed Jul 27, 2026

View reviewed changes

Comment thread src/solvers/blockfv/blockfv_1d.jl

specialize functions for BlockFVO2

ff9371a

jlchan requested changes Aug 4, 2026

View reviewed changes

Comment thread src/solvers/blockfv/blockfv.jl Outdated

Sreeram-Shankar added 2 commits August 4, 2026 20:31

use finite volume reconstruction from subcell

58aa255

Merge branch 'main' into BlockFV-reconstruction

dc758cf

Sreeram-Shankar marked this pull request as ready for review August 5, 2026 01:33

Sreeram-Shankar requested a review from jlchan August 5, 2026 01:33

ranocha requested changes Aug 5, 2026

View reviewed changes

Sreeram-Shankar and others added 3 commits August 14, 2026 18:03

Merge branch 'main' into BlockFV-reconstruction

8fa849e

update finite volume o2 types

fa5d841

Merge branch 'main' into BlockFV-reconstruction

63cbaed

Sreeram-Shankar requested a review from ranocha August 20, 2026 23:16

DanielDoehring requested changes Aug 21, 2026

View reviewed changes

Comment thread src/solvers/blockfv/blockfv.jl

Comment thread src/solvers/blockfv/blockfv_1d.jl

Comment thread src/solvers/blockfv/blockfv_1d.jl

Comment thread src/solvers/blockfv/blockfv_1d.jl

DanielDoehring mentioned this pull request Aug 21, 2026

Move fstar assignment outside loop #3205

Closed

add comments and fix docs issue

d906980

Merge branch 'main' into BlockFV-reconstruction

0f32b37

DanielDoehring added the enhancement New feature or request label Aug 26, 2026

Merge branch 'main' into BlockFV-reconstruction

959daf0

		# Near the element ends the missing neighbor is clamped to the
		# outermost cell (volume-local stencil; no values from other elements).

	"""
	VolumeIntegralPureLGLFiniteVolumeO2(basis;
	volume_flux_fv = flux_lax_friedrichs,
	reconstruction_mode = reconstruction_O2_full,
	slope_limiter = minmod,
	cons2recon = cons2prim,
	recon2cons = prim2cons)

	This gives an up to second order accurate finite volume scheme on an LGL-type subcell
	mesh (LGL = Legendre-Gauss-Lobatto).
	Depending on the `reconstruction_mode` and `slope_limiter`, experimental orders of convergence
	between 1 and 2 can be expected in practice.
	Since this is a volume integral, all reconstructions are purely cell-local, i.e.,
	no neighboring elements are queried at reconstruction stage.

	The interface values of the inner DG-subcells are reconstructed using the standard MUSCL-type reconstruction.
	For the DG-subcells at the boundaries, two options are available:

	1) The unlimited slope is used on these cells.
	This gives full second order accuracy, but also does not damp overshoots between cells.
	The `reconstruction_mode` corresponding to this is `reconstruction_O2_full`.
	2) On boundary subcells, the solution is represented using a constant value, thereby falling back to formally only first order.
	The `reconstruction_mode` corresponding to this is `reconstruction_O2_inner`.
	In the reference below, this is the recommended reconstruction mode and is thus used by default.

	Symmetric total-Variation-Diminishing (TVD) choices for the `slope_limiter` are
	1) [`minmod`](@ref)
	2) [`monotonized_central`](@ref)
	3) [`superbee`](@ref)
	4) [`vanleer`](@ref)
	5) [`koren_symmetric`](@ref)
	Asymmetric TVD limiters are also available, e.g.,
	1) [`koren`](@ref) for positive (right-going) velocities
	2) [`koren_flipped`](@ref) for negative (left-going) velocities

	The reconstruction is performed in reconstruction variables, which default to the primitive variables.
	Other choices are possible, e.g., thermodynamic variables, see [`cons2thermo`](@ref) and [`thermo2cons`](@ref)
	for [`NonIdealCompressibleEulerEquations1D`](@ref) and [`NonIdealCompressibleEulerEquations2D`](@ref).

	!!! note "Conservative systems only"
	Currently only implemented for systems in conservative form, i.e.,
	`have_nonconservative_terms(equations) = False()`

	## References

	See especially Section 3.2, Section 4, and Appendix D of the paper

	- Rueda-Ramírez, Hennemann, Hindenlang, Winters, & Gassner (2021).
	"An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations.
	Part II: Subcell finite volume shock capturing"
	[JCP: 2021.110580](https://doi.org/10.1016/j.jcp.2021.110580)
	"""
	struct VolumeIntegralPureLGLFiniteVolumeO2{SubCellInterfaceCoordinates, VolumeFluxFV,
	Reconstruction, Limiter,
	Cons2Recon, Recon2Cons} <:
	AbstractVolumeIntegralPureLGLFiniteVolume
	sc_interface_coords::SubCellInterfaceCoordinates # (x-)coordinates of the sub-cell element interfaces
	volume_flux_fv::VolumeFluxFV # non-symmetric in general, e.g. entropy-dissipative
	reconstruction_mode::Reconstruction # which type of FV reconstruction to use
	slope_limiter::Limiter # which type of slope limiter function
	cons2recon::Cons2Recon # function to convert from conservative variables to the variables used for reconstruction
	recon2cons::Recon2Cons # function to convert from the variables used for reconstruction back to conservative variables
	end

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