From 873714fff6a956946550f74ffd1f4164a337bad2 Mon Sep 17 00:00:00 2001 From: riccardotosi Date: Tue, 23 Nov 2021 10:05:43 +0100 Subject: [PATCH 1/2] Add space and time tests --- .../space_time_convergence_test/README.md | 39 ++++++++++++++++++ ...convection_diffusion_explicit_solution.jpg | Bin 0 -> 37293 bytes ...ce_error_time_convection_diffusion_bar.jpg | Bin 0 -> 51423 bytes 3 files changed, 39 insertions(+) create mode 100644 convection_diffusion/validation/space_time_convergence_test/README.md create mode 100644 convection_diffusion/validation/space_time_convergence_test/convergence_error_convection_diffusion_explicit_solution.jpg create mode 100644 convection_diffusion/validation/space_time_convergence_test/convergence_error_time_convection_diffusion_bar.jpg diff --git a/convection_diffusion/validation/space_time_convergence_test/README.md b/convection_diffusion/validation/space_time_convergence_test/README.md new file mode 100644 index 00000000..15517a85 --- /dev/null +++ b/convection_diffusion/validation/space_time_convergence_test/README.md @@ -0,0 +1,39 @@ +# Space and time convergence tests + +**Author:** [Riccardo Tosi](https://github.com/riccardotosi) + +**Kratos version:** 9.0 + +**Source files:** [section 2.7 of [1]](https://github.com/KratosMultiphysics/Documentation/blob/master/Resources_files/convection_diffusion_explicit_elements/Eulerian_convection_diffusion_explicit_element.pdf) + +## Space convergence + +We solve the transient convection diffusion equation + and validate its reference implementation. We refer to section 2.7.1 of [1] for details. + +We validate the implementation by computing the norm of the error as , where is the mesh size, and are the analytic and FEM solutions, respectively. + +

+ velocity +

+ +The figure shows that the error converges as expected for both quasi-static ASGS and quasi-static OSS. + +## Time convergence + +We solve the transient convection diffusion equation + and validate its reference implementation. We refer to section 2.7.2 of [1] for details. + +The analytic solution at time is . Therefore, it is possible to compute the norm of the error as +, where is the mesh size, and are the analytic and FEM solutions, respectively. It is expected to obtain an order four accuracy for the Runge-Kutta 4 time integration scheme. + +

+ velocity +

+ +The figure shows that the time accuracy is of order four, as expected. + + +## References + +[1] Tosi, R. (2020). Eulerian convection diffusion explicit elements (p. 27). p. 27. 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z(A&ls_Tz89JN*3_tZUczlnpuF*S54mk{Z741lRg~5U)5*F}qdg`@G01L0RU|W==vZ zr=)@}m0EsK*t4o`2V$w2!Y>aN=P#_zRB69M`T#zhF0ppKTt~(dJfdH>#i=4o-jBgX zN|u&x(f=;d*!{^dZ*y-EMKSsCl)xbVy0%uxrn6rbYbCkDjCn z_1?zJ`pKtNR?e7V+LbWW6?NI`%G(n7F#-lMS*eTi8QhFfa^KJsl;m}}D Date: Tue, 23 Nov 2021 10:08:54 +0100 Subject: [PATCH 2/2] Update READMEs --- README.md | 1 + convection_diffusion/README.md | 1 + convection_diffusion/validation/README.md | 1 + 3 files changed, 3 insertions(+) diff --git a/README.md b/README.md index d4b893e8..a4547929 100644 --- a/README.md +++ b/README.md @@ -161,3 +161,4 @@ Unit tests should *not* be uploaded to this repository. Please put them in the ` - [Convection gaussian hill problem](convection_diffusion/validation/gaussian_hill_explicit) - [Convection-Diffusion gaussian hill problem](convection_diffusion/validation/gaussian_hill_with_diffusion_explicit) - [Rotating pulse problem](convection_diffusion/validation/rotating_pulse_explicit) +- [Space and time convergence tests](convection_diffusion/validation/space_time_convergence_test) \ No newline at end of file diff --git a/convection_diffusion/README.md b/convection_diffusion/README.md index 969a59a8..3dba5045 100644 --- a/convection_diffusion/README.md +++ b/convection_diffusion/README.md @@ -4,3 +4,4 @@ - [Convection gaussian hill problem](validation/gaussian_hill_explicit) - [Convection-Diffusion gaussian hill problem](validation/gaussian_hill_with_diffusion_explicit) - [Rotating pulse problem](validation/rotating_pulse_explicit) +- [Space and time convergence tests](validation/space_time_convergence_test) diff --git a/convection_diffusion/validation/README.md b/convection_diffusion/validation/README.md index dce7bd25..a11aba47 100644 --- a/convection_diffusion/validation/README.md +++ b/convection_diffusion/validation/README.md @@ -5,3 +5,4 @@ This folder contains the validation cases: - [Convection gaussian hill problem](gaussian_hill_explicit) - [Convection-Diffusion gaussian hill problem](gaussian_hill_with_diffusion_explicit) - [Rotating pulse problem](rotating_pulse_explicit) +- [Space and time convergence tests](space_time_convergence_test)