WENO schemes on unstructured meshes using a relaxed a posteriori MOOD limiting approach

In this paper a relaxed formulation of the a posteriori Multi-dimensional Optimal Order Detection (MOOD) limiting approach is introduced for weighted essentially non-oscillatory (WENO) finite volume schemes on unstructured meshes. The main goal is to minimise the computational footprint of the MOOD limiting approach by employing WENO schemes—by virtue of requiring a smaller number of cells to reduce their order of accuracy compared to an unlimited scheme. The key characteristic of the present relaxed MOOD formulation is that the Numerical Admissible Detector (NAD) is not uniquely defined for all orders of spatial accuracy, and it is relaxed when reaching a 2nd-order of accuracy. The augmented numerical schemes are applied to the 2D unsteady Euler equations for a multitude of test problems including the 2D vortex evolution, cylindrical explosion, double-Mach reflection, and an implosion. It is observed that in many events, the implemented MOOD paradigm manages to preserve symmetry of the forming structures in simulations, an improvement comparing to the non-MOOD limited counterparts which cannot be easily obtained due to the multi-dimensional reconstruction nature of the schemes

A relaxed a posteriori MOOD algorithm for multicomponent compressible flows using high-order finite-volume methods on unstructured meshes

In this paper the relaxed, high-order, Multidimensional Optimal Order Detection (MOOD) framework is extended to the simulation of compressible multicomponent flows on unstructured meshes. The diffuse interface methods (DIM) paradigm is used that employs a five-equation model. The implementation is performed in the open-source high-order unstructured compressible flow solver UCNS3D. The high-order CWENO spatial discretisation is selected due to its reduced computational footprint and improved non-oscillatory behaviour compared to the original WENO variant. Fortifying the CWENO method with the relaxed MOOD technique has been necessary to further improve the robustness of the CWENO method. A series of challenging 2-D and 3-D compressible multicomponent flow problems have been investigated, such as the interaction of a shock with a helium bubble, and a water droplet, and the shock-induced collapse of 2-D and 3-D bubbles arrays. Such problems are generally very stiff due to the strong gradients present, and it has been possible to tackle them using the extended MOOD-CWENO numerical framework

UCNS3D: An open-source high-order finite-volume unstructured CFD solver

UCNS3D is an open-source computational solver for compressible flows on unstructured meshes. State-of-the-art high-order methods and their associated benefits can now be implemented for industrial-scale CFD problems due to the flexibility and highly-automated generation offered by unstructured meshes. We present the governing equations of the physical models employed in UCNS3D, and the numerical framework developed for their solution. The code has been designed so that extended to other systems of equations and numerical models is straightforward. The employed methods are validated towards a series of stringent well-established test problems against experimental or analytical solutions, where the full capabilities of UCNS3D in terms of applications spectrum, robustness, efficiency, and accuracy are demonstrated.European Union funding: 314139, 653838 and 823767. Engineering and Physical Sciences Research Council (EPSRC): EP/L000261/1, EP/P020259/1, EP/G069581/1, EP/T518104/1 and 13794 Innovate UK: 26326