Multi-dimensional Optimal Order Detection (MOOD) — a Very High-Order Finite Volume Scheme for Conservation Laws on Unstructured Meshes

A very high-order finite volume method for the time-dependent convection-diffusion problem with Butcher tableau extension ⋮ Direct arbitrary-Lagrangian-Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws ⋮ Neural network-based limiter with transfer learning ⋮ A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation

MOOD

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Application of the principle of minimizing the derivative to the construction of finite-difference schemes for computing discontinuous solutions of gas dynamics. (Reprint)
A high-order finite volume method for systems of conservation laws-multi-dimensional optimal order detection (MOOD)
WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions
A conservative formulation of the multidimensional upwind residual distribution schemes for general nonlinear conservation laws
Spectral (finite) volume method for conservation laws on unstructured grids. II: Extension to two-dimensional scalar equation
Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems
ADER finite volume schemes for nonlinear reaction-diffusion equations
Monoslope and multislope MUSCL methods for unstructured meshes
\(L^{\infty}\) stability of the MUSCL methods
Stabilized residual distribution for shallow water simulations
A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes
ADER schemes on unstructured meshes for nonconservative hyperbolic systems: applications to geophysical flows
The numerical simulation of two-dimensional fluid flow with strong shocks
Efficient implementation of essentially nonoscillatory shock-capturing schemes
TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
Weighted essentially non-oscillatory schemes on triangular meshes
The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
On essentially non-oscillatory schemes on unstructured meshes: Analysis and implementation
Quasi-ENO schemes for unstructured meshes based on umlimited data-dependent least-squares reconstruction
Towards the ultimate conservative difference scheme. II: Monotonicity and conservation combined in a second-order scheme
Entropy splitting and numerical dissipation
Spectral (finite) volume method for conservation laws on unstructured grids. Basic formulation
Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids
ADER schemes for three-dimensional non-linear hyperbolic systems
Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids
Efficient implementation of weighted ENO schemes
Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems
Efficient quadrature-free high-order spectral volume method on unstructured grids: theory and 2D implementation
Essentially non-oscillatory residual distribution schemes for hyperbolic problems
Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids
Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments
High Resolution Schemes and the Entropy Condition
Flow features resulting from shock wave impact on a cylindrical cavity
The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
Uniformly High-Order Accurate Nonoscillatory Schemes. I
TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws
Staggered Lagrangian Discretization Based on Cell-Centered Riemann Solver and Associated Hydrodynamics Scheme
High-Resolution Conservative Algorithms for Advection in Incompressible Flow
High‐order ENO and WENO schemes for unstructured grids
Towards the ultimate conservative difference scheme I. The quest of monotonicity
A technique of treating negative weights in WENO schemes