scholarly journals Doubly-adaptive artificial compression methods for incompressible flow

2020 ◽  
Vol 28 (3) ◽  
pp. 175-192
Author(s):  
William Layton ◽  
Michael McLaughlin
Keyword(s):  
Incompressible Flow ◽  
Second Order ◽  
Compression Method ◽  
Time Step ◽  
First Order ◽  
Numerical Tests ◽  
Compression Parameter ◽  
Artificial Compression ◽  
Artificial Compression Method ◽  
Second Order Methods

AbstractThis report presents adaptive artificial compression methods in which the time-step and artificial compression parameter ε are independently adapted. The resulting algorithms are supported by analysis and numerical tests. The first and second-order methods are embedded. As a result, the computational, cognitive, and space complexities of the adaptive ε, k algorithms are negligibly greater than that of the simplest, first-order, constant ε, constant k artificial compression method.

scholarly journals A First-Order Explicit-Implicit Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 769-782
Author(s):  
Amiya K. Pani ◽  
Vidar Thomée ◽  
A. S. Vasudeva Murthy
Keyword(s):  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Second Order ◽  
Time Step ◽  
Convection Diffusion ◽  
First Order ◽  
Backward Euler ◽  
Strang Splitting ◽  
Spatially Periodic

AbstractWe analyze a second-order in space, first-order in time accurate finite difference method for a spatially periodic convection-diffusion problem. This method is a time stepping method based on the first-order Lie splitting of the spatially semidiscrete solution. In each time step, on an interval of length k, of this solution, the method uses the backward Euler method for the diffusion part, and then applies a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {\frac{k}{m}} for the convection part. With h the mesh width in space, this results in an error bound of the form {C_{0}h^{2}+C_{m}k} for appropriately smooth solutions, where {C_{m}\leq C^{\prime}+\frac{C^{\prime\prime}}{m}}. This work complements the earlier study [V. Thomée and A. S. Vasudeva Murthy, An explicit-implicit splitting method for a convection-diffusion problem, Comput. Methods Appl. Math. 19 2019, 2, 283–293] based on the second-order Strang splitting.

scholarly journals Learned Video Compression via Joint Spatial-Temporal Correlation Exploration

2020 ◽  
Vol 34 (07) ◽  
pp. 11580-11587
Author(s):  
Haojie Liu ◽  
Han Shen ◽  
Lichao Huang ◽  
Ming Lu ◽  
Tong Chen ◽  
...  
Keyword(s):  
Video Coding ◽  
Video Compression ◽  
High Efficiency ◽  
Temporal Correlation ◽  
Second Order ◽  
Compression Method ◽  
High Efficiency Video Coding ◽  
First Order ◽  
Coding Efficiency ◽  
The Common

Traditional video compression technologies have been developed over decades in pursuit of higher coding efficiency. Efficient temporal information representation plays a key role in video coding. Thus, in this paper, we propose to exploit the temporal correlation using both first-order optical flow and second-order flow prediction. We suggest an one-stage learning approach to encapsulate flow as quantized features from consecutive frames which is then entropy coded with adaptive contexts conditioned on joint spatial-temporal priors to exploit second-order correlations. Joint priors are embedded in autoregressive spatial neighbors, co-located hyper elements and temporal neighbors using ConvLSTM recurrently. We evaluate our approach for the low-delay scenario with High-Efficiency Video Coding (H.265/HEVC), H.264/AVC and another learned video compression method, following the common test settings. Our work offers the state-of-the-art performance, with consistent gains across all popular test sequences.

scholarly journals Conservative Transport Schemes for Spherical Geodesic Grids: High-Order Reconstructions for Forward-in-Time Schemes

2010 ◽  
Vol 138 (12) ◽  
pp. 4497-4508 ◽  
Author(s):  
William C. Skamarock ◽  
Maximo Menchaca
Keyword(s):  
Volume Transport ◽  
Higher Order ◽  
Second Order ◽  
Time Step ◽  
First Order ◽  
Order Reconstruction ◽  
Flow Test ◽  
Mesh Density ◽  
Original Scheme ◽  
Dependent Flow

Abstract The finite-volume transport scheme of Miura, for icosahedral–hexagonal meshes on the sphere, is extended by using higher-order reconstructions of the transported scalar within the formulation. The use of second- and fourth-order reconstructions, in contrast to the first-order reconstruction used in the original scheme, results in significantly more accurate solutions at a given mesh density, and better phase and amplitude error characteristics in standard transport tests. The schemes using the higher-order reconstructions also exhibit much less dependence of the solution error on the time step compared to the original formulation. The original scheme of Miura was only tested using a nondeformational time-independent flow. The deformational time-dependent flow test used to examine 2D planar transport in Blossey and Durran is adapted to the sphere, and the schemes are subjected to this test. The results largely confirm those generated using the simpler tests. The results also indicate that the scheme using the second-order reconstruction is most efficient and its use is recommended over the scheme using the first-order reconstruction. The second-order reconstruction uses the same computational stencil as the first-order reconstruction and thus does not create any additional parallelization issues.

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