48 research outputs found
Compressive properties of min-mod-type limiters in modelling shockwave-containing flows
The long-ignored compressive properties of Min-mod-type limiter is investigated in this manuscript by demonstrating its potential in numerically modelling shockwave-containing flows, especially in shock wave/boundary layer interaction (SWBLI) problems. Theoretical studies were firstly performed based on Sweby’s total variation diminishing (TVD) limiter region and Spekreijse’s monotonicity-preserving limiter region to indicate Min-mod-type limiters’ compressive properties. The influence of limiters on the solution accuracy was evaluated using a hybrid-order analysis method based on the grid-independent study in three typical shockwave-containing flows. The conclusions are that, Min-mod-type limiter can be utilized as a dissipative and/or compressive limiter, but depending on the reasonable value of the compression parameter. The compressive Min-mod limiter tends to be more attractive in modelling shockwave-containing flows as compared to other commonly preferred limiters because of its stable computational process and its high-resolution predictions. However, the compressive Min-mod limiter may suffer from its slightly poor convergence, as that observed in other commonly accepted smooth limiters in modelling SWBLI problems. © 2020, The Author(s)
A realtime observatory for laboratory simulation of planetary flows
Motivated by the large-scale circulation of the atmosphere and ocean, we develop a system that uses
observations from a laboratory analog to constrain, in real time, a numerical simulation of the laboratory
flow. This system provides a tool to rapidly prototype new methods for state and parameter
estimation, and facilitates the study of prediction, predictability, and transport of geophysical fluids
where observations or numerical simulations would not independently suffice.
A computer vision system is used to extract measurements of the physical simulation. Observations
are used to constrain the model-state of the MIT General Circulation Model in a probabilistic, ensemble based assimilation approach. Using a combination of parallelism, domain decomposition and an efficient
scheme to select ensembles of model-states, we show that estimates that effectively track the fluid state
can be produced. To the best of our knowledge this is the first such observatory for laboratory
analogs of planetary circulation that functions in real time.National Science Foundation (U.S.) (CNS-0540259)National Science Foundation (U.S.) (grant CNS-0540248
A non-linear multigrid method for the steady Euler equations
Higher-order accurate Euler-flow solutions are presented for some airfoil test cases. Second-order accurate solutions are computed by an Iterative Defect Correction process. For two test cases even higher accuracy is obtained by the additional use of a ~xtrapolation technique. Finite volume Osher-type discretizations are applied throughout. Two interpolation schemes (one with and one w~hout a flux limiter) are used for the computation of the second-order defect. In each Defect Correction cycle, the solution is computed by non-linear mu~igrid iteration, in which Collective Symmetric Gauss-Seidel relaxation is used as the smoothing procedure. The computational method does not require tuning of parameters. The solutions show a good resolution of discontinuities, and they are obtained at low computational costs. The rate of convergence seems to be grid-independent
On the Nonlinearity of Modern Shock-Capturing Schemes
The development is reviewed of shock capturing methods, paying special attention to the increasing nonlinearity in the design of numerical schemes. The nature is studies of this nonlinearity and its relation to upwind differencing is examined. This nonlinearity of the modern shock capturing methods is essential, in the sense that linear analysis is not justified and may lead to wrong conclusions. Examples to demonstrate this point are given