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Flow in fractured porous media occurs in the earth's subsurface, in biological tissues, and in man-made materials. Fractures have a dominating influence on flow processes, and the last decade has seen an extensive development of models and numerical methods that explicitly account for their presence. To support these developments, we present a portfolio of four benchmark cases for single-phase flow in three-dimensional fractured porous media. The cases are specifically designed to test the methods' capabilities in handling various complexities common to the geometrical structures of fracture networks. Based on an open call for participation, results obtained with 17 numerical methods were collected. This paper presents the underlying mathematical model, an overview of the features of the participating numerical methods, and their performance in solving the benchmark cases.

Most encrypted data formats leak metadata via their plaintext headers, such as format version, encryption schemes used, number of recipients who can decrypt the data, and even the recipients' identities. This leakage can pose security and privacy risks to users, e.g., by revealing the full membership of a group of collaborators from a single encrypted e-mail, or by enabling an eavesdropper to fingerprint the precise encryption software version and configuration the sender used. We propose that future encrypted data formats improve security and privacy hygiene by producing $\textit{Padded Uniform Random Blobs}$ or PURBs: ciphertexts indistinguishable from random bit strings to anyone without a decryption key. A PURB's content leaks $\textit{nothing at all}$, even the application that created it, and is padded such that even its length leaks as little as possible. Encoding and decoding ciphertexts with $\textit{no}$ cleartext markers presents efficiency challenges, however. We present cryptographically agile encodings enabling legitimate recipients to decrypt a PURB efficiently, even when encrypted for any number of recipients' public keys and/or passwords, and when these public keys are from different cryptographic suites. PURBs employ Padm\'e, a~novel padding scheme that limits information leakage via ciphertexts of maximum length $M$ to a practical optimum of $O(\log \log M)$ bits, comparable to padding to a power of two, but with lower overhead of at most $12\%$ and decreasing with larger payloads., Comment: 30 pages

The paper develops a method for the numerical simulation of a free-surface flow of incompressible viscous fluid around a streamlined body. The body is a rigid stationary construction partially submerged in the fluid. The application we are interested in the paper is a flow around a surface mounted offshore oil platform. The numerical method builds on a hybrid finite volume / finite difference discretization using adaptive octree cubic meshes. The mesh is dynamically refined towards the free surface and the construction. Special care is taken to devise a discretization for the case of curvilinear boundaries and interfaces immersed in the octree Cartesian background computational mesh. To demonstrate the accuracy of the method, we show the results for two benchmark problems: the sloshing 3D container and the channel laminar flow passing the 3D cylinder of circular cross-section. Further, we simulate numerically a flow with surface waves around an offshore oil platform for the realistic set of geophysical data.