Solving One Dimensional Scalar Conservation Laws by Particle Management

We present a meshfree numerical solver for scalar conservation laws in one space dimension. Points representing the solution are moved according to their characteristic velocities. Particle interaction is resolved by purely local particle management. Since no global remeshing is required, shocks stay sharp and propagate at the correct speed, while rarefaction waves are created where appropriate. The method is TVD, entropy decreasing, exactly conservative, and has no numerical dissipation. Difficulties involving transonic points do not occur, however inflection points of the flux function pose a slight challenge, which can be overcome by a special treatment. Away from shocks the method is second order accurate, while shocks are resolved with first order accuracy. A postprocessing step can recover the second order accuracy. The method is compared to CLAWPACK in test cases and is found to yield an increase in accuracy for comparable resolutions.Comment: 15 pages, 6 figures. Submitted to proceedings of the Fourth International Workshop Meshfree Methods for Partial Differential Equation

High Order Upwind Schemes for Multidimensional Magnetohydrodynamics

A general method for constructing high order upwind schemes for multidimensional magnetohydrodynamics (MHD), having as a main built-in condition the divergence-free constraint \divb=0 for the magnetic field vector \bb, is proposed. The suggested procedure is based on {\em consistency} arguments, by taking into account the specific operator structure of MHD equations with respect to the reference Euler equations of gas-dynamics. This approach leads in a natural way to a staggered representation of the \bb field numerical data where the divergence-free condition in the cell-averaged form, corresponding to second order accurate numerical derivatives, is exactly fulfilled. To extend this property to higher order schemes, we then give general prescriptions to satisfy a $(r+1)^{th}$ order accurate \divb=0 relation for any numerical \bb field having a $r^{th}$ order interpolation accuracy. Consistency arguments lead also to a proper formulation of the upwind procedures needed to integrate the induction equations, assuring the exact conservation in time of the divergence-free condition and the related continuity properties for the \bb vector components. As an application, a third order code to simulate multidimensional MHD flows of astrophysical interest is developed using ENO-based reconstruction algorithms. Several test problems to illustrate and validate the proposed approach are finally presented.Comment: 34 pages, including 14 figure

Dispersive wave runup on non-uniform shores

Historically the finite volume methods have been developed for the numerical integration of conservation laws. In this study we present some recent results on the application of such schemes to dispersive PDEs. Namely, we solve numerically a representative of Boussinesq type equations in view of important applications to the coastal hydrodynamics. Numerical results of the runup of a moderate wave onto a non-uniform beach are presented along with great lines of the employed numerical method (see D. Dutykh et al. (2011) for more details).Comment: 8 pages, 6 figures, 18 references. This preprint is submitted to FVCA6 conference proceedings. Other author papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh

A rarefaction-tracking method for hyperbolic conservation laws

We present a numerical method for scalar conservation laws in one space dimension. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction and compression waves. The solution is represented by particles that carry function values and move according to the method of characteristics. Between two neighboring particles, an interpolation is defined by an analytical similarity solution of the conservation law. An interaction of particles represents a collision of characteristics. The resulting shock is resolved by merging particles so that the total area under the function is conserved. The method is variation diminishing, nevertheless, it has no numerical dissipation away from shocks. Although shocks are not explicitly tracked, they can be located accurately. We present numerical examples, and outline specific applications and extensions of the approach.Comment: 21 pages, 7 figures. Similarity 2008 conference proceeding

Observations of Aerosol-Radiation-Cloud Interactions in the South-East Atlantic: First Results from the ORACLES Deployments in 2016 and 2017

Southern Africa produces almost a third of the Earths biomass burning (BB) aerosol particles. Particles lofted into the mid-troposphere are transported westward over the South-East (SE) Atlantic, home to one of the three permanent subtropical stratocumulus (Sc) cloud decks in the world. The SE Atlantic stratocumulus deck interacts with the dense layers of BB aerosols that initially overlay the cloud deck, but later subside and often mix into the clouds. These interactions include adjustments to aerosol-induced solar heating and microphysical effects, and their global representation in climate models remains one of the largest uncertainties in estimates of future climate. Hence, new observations over the SE Atlantic have significant implications for regional and global climate change predictions.The low-level clouds in the SE Atlantic have limited vertical extent and therefore present favorable conditions for their exploration with remote sensing. On the other hand, the normal coexistence of BB aerosols and Sc clouds in the same scene also presents significant challenges to conventional remote sensing techniques. We describe first results from NASAs airborne ORACLES (ObseRvations of Aerosols Above Clouds and Their IntEractionS) deployments in September 2016 and August 2017. We emphasize the unique role of polarimetric observations by two instruments, the Research Scanning Polarimeter (RSP) and the Airborne Multi-angle SpectroPolarimeter Imager (AirMSPI), and describe how these instruments help address specific ORACLES science objectives. Initial assessments of polarimetric observation accuracy for key cloud and aerosol properties will be presented, in as far as the preliminary nature of measurements permits

An Euler Solver Based on Locally Adaptive Discrete Velocities

A new discrete-velocity model is presented to solve the three-dimensional Euler equations. The velocities in the model are of an adaptive nature---both the origin of the discrete-velocity space and the magnitudes of the discrete-velocities are dependent on the local flow--- and are used in a finite volume context. The numerical implementation of the model follows the near-equilibrium flow method of Nadiga and Pullin [1] and results in a scheme which is second order in space (in the smooth regions and between first and second order at discontinuities) and second order in time. (The three-dimensional code is included.) For one choice of the scaling between the magnitude of the discrete-velocities and the local internal energy of the flow, the method reduces to a flux-splitting scheme based on characteristics. As a preliminary exercise, the result of the Sod shock-tube simulation is compared to the exact solution.Comment: 17 pages including 2 figures and CMFortran code listing. All in one postscript file (adv.ps) compressed and uuencoded (adv.uu). Name mail file `adv.uu'. Edit so that `#!/bin/csh -f' is the first line of adv.uu On a unix machine say `csh adv.uu'. On a non-unix machine: uudecode adv.uu; uncompress adv.tar.Z; tar -xvf adv.ta

A characteristic particle method for traffic flow simulations on highway networks

A characteristic particle method for the simulation of first order macroscopic traffic models on road networks is presented. The approach is based on the method "particleclaw", which solves scalar one dimensional hyperbolic conservations laws exactly, except for a small error right around shocks. The method is generalized to nonlinear network flows, where particle approximations on the edges are suitably coupled together at the network nodes. It is demonstrated in numerical examples that the resulting particle method can approximate traffic jams accurately, while only devoting a few degrees of freedom to each edge of the network.Comment: 15 pages, 5 figures. Accepted to the proceedings of the Sixth International Workshop Meshfree Methods for PDE 201

Study protocol: an evaluation of the effectiveness, experiences and costs of a patient-directed strategy compared with a multi-faceted strategy to implement physical cancer rehabilitation programmes for cancer survivors in a European healthcare system; a controlled before and after study

Background The need for physical cancer rehabilitation programmes (PCRPs), addressing adverse effects from cancer, is growing. Implementing these programmes into daily practice is still a challenge. Since barriers for successful implementation often arise at different levels in healthcare, multi-faceted strategies focusing on multiple levels are likely more effective than single-faceted strategies. Nevertheless, most studies implementing PCRPs used strategies directed at patients only. The aim of this study is to develop and identify the most effective strategy to implement PCRPs into daily care. We want to assess the added value of a multi-faceted strategy compared with a single-faceted patient-directed strategy. Methods/design We will conduct a clustered controlled before and after study (CBA) in the Netherlands that compares two strategies to implement PCRPs. The patient-directed (PD) strategy (five hospitals) will focus on change at the patient level. The multi-faceted (MF) strategy (five hospitals) will focus on change at the patient, professional and organizational levels. Eligibility criteria are as follows: (A) patients: adults; preferably (history of) cancer in the gastro-intestinal, reproductive and/or urological system; successful primary treatment; and without recurrence/metastases. (B) Healthcare professionals: involved in cancer care. A stepwise approach will be followed: Step 1: Analysis of the current implementation of PCRPs and the examination of barriers and facilitators for implementation, via a qualitative study with patients (four focus groups n = 10–12) and their healthcare workers (four focus groups n = 10–12 and individual interviews n = 30–40) and collecting data on adherence to quality indicators (n = 500 patients, 50 per hospital). Step 2: Selection and development of interventions to create a PD and MF strategy during expert roundtable discussions, using the knowledge gained in step 1 and a literature search of the effect of strategies for implementing PCRPs. Step 3: Test and compare both strategies with a clustered CBA (effectiveness, process evaluation and costs), by data extraction from existing registration systems, questionnaires and interviews. For the effectiveness and cost-effectiveness, n = 500 patients, 50 per hospital. For the process evaluation, n = 50 patients, 5 per hospital, and n = 40 healthcare professionals, 4 per hospital. Main outcome measures: % screened patients, % referrals to PCRPs, incremental costs and incremental cost-effectiveness ratios (ICERs)