{"id":32578328,"url":"https://github.com/hugomvale/hr-weno","last_synced_at":"2026-02-25T18:03:42.916Z","repository":{"id":59594332,"uuid":"220562554","full_name":"HugoMVale/HR-WENO","owner":"HugoMVale","description":"A Fortran implementation of high-resolution WENO schemes for hyperbolic conservation equations 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HR-WENO (High-Resolution Weighted Essentially Non-Oscillatory)\n\n[![test](https://github.com/HugoMVale/HR-WENO/actions/workflows/test.yml/badge.svg)](https://github.com/HugoMVale/HR-WENO/actions)\n[![codecov](https://codecov.io/gh/HugoMVale/HR-WENO/branch/main/graph/badge.svg?token=1XL5LQSO9P)](https://codecov.io/gh/HugoMVale/HR-WENO)\n[![Language](https://img.shields.io/badge/-Fortran-734f96?logo=fortran\u0026logoColor=white)](https://github.com/topics/fortran)\n[![Ask DeepWiki](https://deepwiki.com/badge.svg)](https://deepwiki.com/HugoMVale/HR-WENO)\n\n\u003cp align=\"center\"\u003e\n  \u003cimg src=\"output/example1/example1d.gif\" width=\"500\" alt=\"Solution of Burger's equation with 5th order WENO\"\u003e\n\u003c/p\u003e\n\n## Description\n\nThis package is a modern-Fortran implementation of selected high-resolution [weighted essentially non-oscillatory (WENO)](https://en.wikipedia.org/wiki/WENO_methods) schemes and [total variation diminishing (TVD)](https://en.wikipedia.org/wiki/Total_variation_diminishing) integration methods for solving [hyperbolic conservation equations](https://en.wikipedia.org/wiki/Hyperbolic_partial_differential_equation).\n\nIn particular, the package includes:\n\n* WENO schemes up to 5th order;\n* explicit Runge-Kutta TVD methods up to 3rd order;\n* explicit 3rd order multi-step TVD method.  \n\nAll numerical methods are described in detail by [Shu (1997)](doc/Shu-WENO-notes.pdf).\n\n## Documentation\n\n* This readme (start with that).\n* [API Reference](https://hugomvale.github.io/HR-WENO/).\n\n## Getting started\n\n### Build\n\nThe easiest way to build/test the code and run the examples is by means of [`fpm`](https://fpm.fortran-lang.org/en/index.html). To run a given example, just do:\n\n```sh\nfpm run --example \"example-filename\" --profile release\n```\n\nand the numerical results will be stored in the [`output`](/output) subfolder. You can then use the provided Python script to read the data and plot the results.\n\n### Usage\n\nThe ODE solvers (`rktvd` and `mstvd`) are called like most other solvers (e.g., LSODE): \n\n```fortran\nuse tvdode, only: rktvd\n...\ntype(rktvd) :: ode\n...\n! Initialize solver object\node = rktvd(rhs, neq=size(u), order=3)\n\n! Integrate\ntime_start = 0.0_rk\ntime_end = 12.0_rk\ndt = 1e-2_rk\ntime = time_start\nnum_time_points = 100\ndo i = 0, num_time_points\n  time_out = time_end*i/num_time_points\n  call ode%integrate(u, time, time_out, dt)\n  call save_intermediate_results(u, time, ...)\nend do\n ...\n ```\n\n The WENO reconstruction is even simpler to call:\n\n ```fortran\nuse hrweno, only: weno\n...\ntype(weno) :: myweno\n...\n! Initialize weno object\nmyweno = weno(ncells=100, k=3, eps=1e-6_rk)\n   \n! Get reconstructed values at cell boundaries\ncall myweno%reconstruct(v, vl, vr)\n...\n```\n\n## Examples\n\n### Burgers' inviscid equation (1D)\n\nThis example ([`example1_burgers_1d_fv.f90`](/example/example1_burgers_1d_fv.f90)) illustrates the application of procedures `weno` and `rktvd` for solving [Burger's inviscid equation](https://en.wikipedia.org/wiki/Burgers%27_equation) using a finite volume (FV) formulation. The results are depicted in the figure at the top of the page and demonstrate the excellent resolution of the shock wave.\n\n### Population balance equation (2D)\nThis example ([`example2_pbe_2d_fv.f90`](/example/example2_pbe_2d_fv.f90)) illustrates the application of procedures `weno` and `mstvd` for solving a [population balance equation](https://en.wikipedia.org/wiki/Population_balance_equation) with 2 internal coordinates using a finite volume (FV) formulation. The results are depicted in the figure below and demonstrate the excellent resolution of the pulse.\n\n\u003cp align=\"center\"\u003e\n  \u003cimg src=\"output/example2/example2d.gif\" width=\"600\" alt=\"Solution of 2D PBE with 5th order WENO\"\u003e\n\u003c/p\u003e\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fhugomvale%2Fhr-weno","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fhugomvale%2Fhr-weno","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fhugomvale%2Fhr-weno/lists"}