scholarly journals Towards an Unstaggered Finite‐Volume Dynamical Core With a Fast Riemann Solver: 1‐D Linearized Analysis of Dissipation, Dispersion, and Noise Control

2018 ◽  
Vol 10 (9) ◽  
pp. 2333-2356 ◽  
Author(s):  
Xi Chen ◽  
Shiann‐Jiann Lin ◽  
Lucas M. Harris
Keyword(s):  
Finite Volume ◽  
Noise Control ◽  
Riemann Solver ◽  
Dynamical Core

Transport Schemes in GungHo

2021 ◽  
Author(s):  
James Kent
Keyword(s):  
Finite Element ◽  
Finite Volume ◽  
Mixed Finite Element ◽  
Method Of Lines ◽  
Finite Volume Methods ◽  
Kutta Method ◽  
Finite Volume Schemes ◽  
Dynamical Core ◽  
Runge Kutta Method ◽  
The Stability

<p>GungHo is the mixed finite-element dynamical core under development by the Met Office. A key component of the dynamical core is the transport scheme, which advects density, temperature, moisture, and the winds, throughout the atmosphere. Transport in GungHo is performed by finite-volume methods, to ensure conservation of certain quantaties. There are a range of different finite-volume schemes being considered for transport, including the Runge-Kutta/method-of-lines and COSMIC/Lin-Rood schemes. Additional horizontal/vertical splitting approaches are also under consideration, to improve the stability aspects of the model. Here we discuss these transport options and present results from the GungHo framework, featuring both prescribed velocity advection tests and full dry dynamical core tests. </p>

The Suliciu approximate Riemann solver is not invariant domain preserving

2019 ◽  
Vol 16 (01) ◽  
pp. 59-72 ◽  
Author(s):  
Jean-Luc Guermond ◽  
Christian Klingenberg ◽  
Bojan Popov ◽  
Ignacio Tomas
Keyword(s):  
Finite Volume ◽  
Riemann Solver ◽  
Approximate Riemann Solver ◽  
Invariant Domain ◽  
First Order

We show that the first-order finite volume technique based on the Suliciu approximate Riemann solver, while being positive, violates the invariant domain properties of the [Formula: see text]-system.

scholarly journals A Multimoment Constrained Finite-Volume Model for Nonhydrostatic Atmospheric Dynamics

2013 ◽  
Vol 141 (4) ◽  
pp. 1216-1240 ◽  
Author(s):  
Xingliang Li ◽  
Chungang Chen ◽  
Xueshun Shen ◽  
Feng Xiao
Keyword(s):  
Finite Volume ◽  
Evolution Equations ◽  
Complex Geometry ◽  
High Order ◽  
Computationally Efficient ◽  
Dynamical Core ◽  
Benchmark Tests ◽  
Volume Method ◽  
Further Development ◽  
Mesh Cell

Abstract The two-dimensional nonhydrostatic compressible dynamical core for the atmosphere has been developed by using a new nodal-type high-order conservative method, the so-called multimoment constrained finite-volume (MCV) method. Different from the conventional finite-volume method, the predicted variables (unknowns) in an MCV scheme are the values at the solution points distributed within each mesh cell. The time evolution equations to update the unknown point values are derived from a set of constraint conditions based on the multimoment concept, where the constraint on the volume-integrated average (VIA) for each mesh cell is cast into a flux form and thus guarantees rigorously the numerical conservation. Two important features make the MCV method particularly attractive as an accurate and practical numerical framework for atmospheric and oceanic modeling. 1) The predicted variables are the nodal values at the solution points that can be flexibly located within a mesh cell (equidistant solution points are used in the present model). It is computationally efficient and provides great convenience in dealing with complex geometry and source terms. 2) High-order and physically consistent formulations can be built by choosing proper constraints in view of not only numerical accuracy and efficiency but also underlying physics. In this paper the authors present a dynamical core that uses the third- and the fourth-order MCV schemes. They have verified the numerical outputs of both schemes by widely used standard benchmark tests and obtained competitive results. The present numerical core provides a promising and practical framework for further development of nonhydrostatic compressible atmospheric models.

A High Order Sharp-Interface Method with Local Time Stepping for Compressible Multiphase Flows

2011 ◽  
Vol 9 (1) ◽  
pp. 205-230 ◽  
Author(s):  
Angela Ferrari ◽  
Claus-Dieter Munz ◽  
Bernhard Weigand
Keyword(s):  
Finite Volume ◽  
High Order ◽  
Indicator Function ◽  
Finite Volume Scheme ◽  
Riemann Solver ◽  
Time Step ◽  
Material Interface ◽  
Volume Scheme ◽  
Time Stepping ◽  
Local Time Stepping

AbstractIn this paper, a new sharp-interface approach to simulate compressible multiphase flows is proposed. The new scheme consists of a high order WENO finite volume scheme for solving the Euler equations coupled with a high order path-conservative discontinuous Galerkin finite element scheme to evolve an indicator function that tracks the material interface. At the interface our method applies ghost cells to compute the numerical flux, as the ghost fluid method. However, unlike the original ghost fluid scheme of Fedkiw et al. [15], the state of the ghost fluid is derived from an approximate-state Riemann solver, similar to the approach proposed in [25], but based on a much simpler formulation. Our formulation leads only to one single scalar nonlinear algebraic equation that has to be solved at the interface, instead of the system used in [25]. Away from the interface, we use the new general Osher-type flux recently proposed by Dumbser and Toro [13], which is a simple but complete Riemann solver, applicable to general hyperbolic conservation laws. The time integration is performed using a fully-discrete one-step scheme, based on the approaches recently proposed in [5,7]. This allows us to evolve the system also with time-accurate local time stepping. Due to the sub-cell resolution and the subsequent more restrictive time-step constraint of the DG scheme, a local evolution for the indicator function is applied, which is matched with the finite volume scheme for the solution of the Euler equations that runs with a larger time step. The use of a locally optimal time step avoids the introduction of excessive numerical diffusion in the finite volume scheme. Two different fluids have been used, namely an ideal gas and a weakly compressible fluid modeled by the Tait equation. Several tests have been computed to assess the accuracy and the performance of the new high order scheme. A verification of our algorithm has been carefully carried out using exact solutions as well as a comparison with other numerical reference solutions. The material interface is resolved sharply and accurately without spurious oscillations in the pressure field.

An accurate shock-capturing scheme based on rotated-hybrid Riemann solver

2016 ◽  
Vol 26 (5) ◽  
pp. 1310-1327 ◽  
Author(s):  
Ghislain Tchuen ◽  
Pascalin Tiam Kapen ◽  
Yves Burtschell
Keyword(s):  
Compressible Flow ◽  
Finite Volume ◽  
Compressible Flows ◽  
Navier Stokes ◽  
Shock Propagation ◽  
Riemann Solver ◽  
Simple Task ◽  
Content Type ◽  
Flow Problems ◽  
Roe Solver

Purpose – The purpose of this paper is to present a new hybrid Euler flux fonction for use in a finite-volume Euler/Navier-Stokes code and adapted to compressible flow problems. Design/methodology/approach – The proposed scheme, called AUFSRR can be devised by combining the AUFS solver and the Roe solver, based on a rotated Riemann solver approach (Sun and Takayama, 2003; Ren, 2003). The upwind direction is determined by the velocity-difference vector and idea is to apply the AUFS solver in the direction normal to shocks to suppress carbuncle and the Roe solver across shear layers to avoid an excessive amount of dissipation. The resulting flux functions can be implemented in a very simple manner, in the form of the Roe solver with modified wave speeds, so that converting an existing AUFS flux code into the new fluxes is an extremely simple task. Findings – The proposed flux functions require about 18 per cent more CPU time than the Roe flux. Accuracy, efficiency and other essential features of AUFSRR scheme are evaluated by analyzing shock propagation behaviours for both the steady and unsteady compressible flows. This is demonstrated by several test cases (1D and 2D) with standard finite-volume Euler code, by comparing results with existing methods. Practical implications – The hybrid Euler flux function is used in a finite-volume Euler/Navier-Stokes code and adapted to compressible flow problems. Originality/value – The AUFSRR scheme is devised by combining the AUFS solver and the Roe solver, based on a rotated Riemann solver approach.

Application of a Riemann Solver Unstructured Finite Volume Method to Combustion Instabilities

2015 ◽  
Vol 31 (3) ◽  
pp. 937-950 ◽  
Author(s):  
Perry L. Johnson ◽  
Jared M. Pent ◽  
Hrvoje Jasak ◽  
J. Enrique Portillo
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Riemann Solver ◽  
Combustion Instabilities ◽  
Volume Method ◽  
Unstructured Finite Volume Method

Exploring Convection-Allowing Model Evaluation Strategies for Severe Local Storms Using the Finite-Volume Cubed-Sphere (FV3) Model Core

2021 ◽  
Vol 36 (1) ◽  
pp. 3-19
Author(s):  
Burkely T. Gallo ◽  
Jamie K. Wolff ◽  
Adam J. Clark ◽  
Israel Jirak ◽  
Lindsay R. Blank ◽  
...  
Keyword(s):  
Finite Volume ◽  
Weather Forecasting ◽  
Severe Weather ◽  
Receiver Operating Curve ◽  
Brier Score ◽  
Dynamical Core ◽  
Object Based ◽  
Verification Methods ◽  
Cubed Sphere ◽  
Verification Techniques

AbstractVerification methods for convection-allowing models (CAMs) should consider the finescale spatial and temporal detail provided by CAMs, and including both neighborhood and object-based methods can account for displaced features that may still provide useful information. This work explores both contingency table–based verification techniques and object-based verification techniques as they relate to forecasts of severe convection. Two key fields in severe weather forecasting are investigated: updraft helicity (UH) and simulated composite reflectivity. UH is used to generate severe weather probabilities called surrogate severe fields, which have two tunable parameters: the UH threshold and the smoothing level. Probabilities computed using the UH threshold and smoothing level that give the best area under the receiver operating curve result in very high probabilities, while optimizing the parameters based on the Brier score reliability component results in much lower probabilities. Subjective ratings from participants in the 2018 NOAA Hazardous Weather Testbed Spring Forecasting Experiment (SFE) provide a complementary evaluation source. This work compares the verification methodologies in the context of three CAMs using the Finite-Volume Cubed-Sphere Dynamical Core (FV3), which will be the foundation of the U.S. Unified Forecast System (UFS). Three agencies ran FV3-based CAMs during the five-week 2018 SFE. These FV3-based CAMs are verified alongside a current operational CAM, the High-Resolution Rapid Refresh version 3 (HRRRv3). The HRRR is planned to eventually use the FV3 dynamical core as part of the UFS; as such evaluations relative to current HRRR configurations are imperative to maintaining high forecast quality and informing future implementation decisions.

Sign in / Sign up

Export Citation Format

Share Document